oh hey, i'm in a very similar situation (182cm/53kg, according to the multiple nutritionists i've worked with i apparently need to be downing 4'500-5'000 kcal/day even without exercise). now, i'm nowhere near that point yet, but i have managed to get myself up to about 3'500 kcal/day without needing to vomit from the sheer volume of food in my stomach, so maybe this'll be helpful :)
here's my thoughts and tips, in no particular order:

first of all, there's plenty you can do without even having to modify an existing diet that much. oils and other fats are extremely calorie-dense, and you can easily add more of them to a dish you were gonna make anyway. making pasta bolognese? slather the pasta in olive oil before adding the sauce and boom, you've just added like 100 kcal per serving! making toast? you can easily slap like 70 kcal worth of butter on there. a single spoonful of peanut butter is 100 kcal, spread some generously on some crackers or use it as a dip and you've just made a multi-hundred kcal snack which you can down in just a few bites.

you mentioned ice cream... ice cream is decently calorie-dense, but isn't great and IME tends to be hard to eat a lot of (especially if it has a lot of sugar, which most ice creams do). i certainly wouldn't rely on it as a primary source of additional calories; you're trying to eat an additional 1'600 kcal/day and, to the shock and dismay of 10-year-olds everywhere, eating that much ice cream every day will rapidly become a chore and then pure torture. what it is useful for is smoothies!

smoothies (or any other kind of liquid calories) are your friend because of the very simple fact that it's much easier to just fuckin chug them even if you aren't that hungry -- or, better yet, right after eating a regular meal to "fill in the cracks". if you have a blender they're super easy to make, and generally don't require a lot of expensive ingredients (normally you've got milk or ice cream as a base, plus maybe some sugar and/or (frozen) berries and/or peanut butter and/or whatever other bullshit you have on hand!). you can also just get them pre-made; for example my school cafeteria sells yfood smoothies at a discount and i've been buying them to add 500 kcal to my lunch every day for a relatively modest increase in price. there's also smoothie powder you can get in bulk (mainly intended for protein shakes), but personally i find that those taste pretty gross.

might update this post later if i think of anything more :3

EDIT: oh yeah, consider getting fiber supplements or similar, because after eating a bunch of "food that makes you fat" you likely will have a hard time finding space in your stomach for "food that helps you poop" and end up making yourself very constipated.