Drain and rinse beans. Toss into a medium bowl with drained corn. Chop tomato and onion; add to beans along with parsley. Season with salt and pepper and toss to combine. Divide between 4 tortillas. Sprinkle with shredded cheese and roll up tightly with ends tucked in.
Serve burritos with honeydew slices, sugar snap peas and a few slices of avocado on the side.