That's not really a banh mi, banh mi is on a French roll, typically with mayo, paté, various protein options (Vietnamese cold cuts are common, grilled pork/chicken, meatballs/sausage, tofu, etc), pickled carrots and daikon radish, cucumber, cilantro, and jalapeños. At least from my experience. I'm not sure how strict a definition it has, but it definitely comes on a French roll. They're absolutely delicious, I highly recommend you try one! That other sandwich sounds good too though.