I have a farm share (CSA). At the start of the year, you pay up front for a share; in return, you get boxes of veggies during the season. Since the farmer is paid up front, they don't need to borrow money from the bank and hope for a decent harvest to repay the loan, so there's less pressure on them: they know their farm will still be around next year. And you get boxes of veggies that were picked within the past 24 hours, so they're all incredibly fresh. You'll get some stuff you can find in the grocery store (ex: roma tomatoes, bell peppers) but since all the middlemen have been cut out, they last a long time (I've had heads of lettuce last like a month); and you'll get some that's either heirloom varieties (too fragile for handling by the supply chain feeding grocery stores) or unusual (ex: pawpaws, ground cherries).
I'm going to say up front that a farm share isn't for everyone; it takes some adjustment and a bit of work to make it work well, but for me it's worth it. I'll note that I'm single (so it all falls on me) and vegetarian (so I can sometimes eat a lot of veggies).
Each farm chooses how to operate, so I can only speak in generalities. To accommodate different family sizes, some farms offer boxes of different sizes/prices; others offer a half-share, so instead of getting a box every week for 20-26 weeks, you get a box for 10-13 weeks (you choose which weeks you want a box). You can also find a friend to split the cost and content of a share, either splitting each box, or alternating pickup weeks.
Some farms will pre-pack the boxes for you; others will put the veggies on a table and let you choose among them; for example, this week's share might be something like "choose 3 zucchinis/eggplants; choose 2 lbs of a bunch of different types of tomatoes; choose 4 varieties of hot peppers", etc. Some farms you have to pick up at the farm itself; other farms have distribution points in outlying areas, will let you pick up at local farmers markets, or have home delivery for an additional fee. Some farms have work shares: instead of paying for a share, you can choose to work like 4 hours a week during the season and get a box of veggies each week in return. Most farms have pick-your-own availability for veggies that may not be to everyone's taste (okra, herbs), where some people may want extras (tomatoes, peppers, beans), or where personal taste is important (flowers).
I've been with a bunch of different farms over the years (I've moved several times; and sometimes I've joined a farm that isn't a great fit for me). For the past couple years, I've been getting my own box instead of splitting a share, and I've opted to get a 10-week share (I choose the weeks). One thing I like with the 10-week share is that I'm not facing fresh veggies to work with every week; sometimes a weekly share can seem overwhelming!
Most people make some adaptations to make a CSA work for them. It's taken me a while, but I've finally come up with a set a recipes for stuff that I like, that uses the veggies I tend to get, much of which stores well; and I have a pattern of processing that works for me:
Each week, the farm sends out an email ahead of time, letting you know what's in season and sometimes with a rough idea of how much to expect ("this'll be the last week for blackberries, but we have lots of tomatoes!"); that helps me plan what to do ahead of time.
On weeks that I have a share, I go to the farm, do the PYO (it's included in my share, and my starving Irish ancestors would be upset if I didn't get them!), and choose the veggies for my box. When I get home, I wash everything, then sit in front of the tv, watching my guilty-pleasure shows and processing the veggies - as applicable, I trim, peel, slice, dice, mince, etc. As I finish each veggie, it goes into a sealed bowl or a Ziploc and goes into the fridge. I also have a spare bowl for scraps - ends and peels of onions and carrots, trimmings from peppers and leeks, etc. Those join other scraps in a big Ziploc in the freezer; when I have enough scraps, I use it to make veggie stock. And there's another bowl for stuff I can't use, that either goes in the garbage or a compost pile (I've stopped composting in recent years).
On Saturday, I spend a couple hours cooking, usually 2-3 big dishes or 4-5 smaller ones - it depends on my mood and what's in season. Then half the food gets portion-sized and frozen; the other half gets eaten over the week or so following. While cooking, I may pickle some veggies. Pickling is easy: you put your chosen veggies and spices in a jar, heat up your pickling brine, pour the brine over the veggies, and seal the jar. During a season, I may pickle dilly beans, beets, giardinieri, garlic, onions, cucumbers, etc; I may eat them out of the jar or use them as ingredients in future dishes.
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