Set your oven to 400 degrees Fahrenheit and let it fully heat while you prep everything else. A properly hot oven is what gives the tops of these burritos that light golden color once the cheese melts. Don't skip this step even if you're in a hurry, since a lukewarm oven leads to soggy tortillas instead of a lightly crisp finish.
In a large bowl, stir together the refried beans, cooked rice, salsa, green chilies, corn, and one cup of the shredded cheese. If you're adding chicken, pull out a portion of the mix into a separate bowl and stir the chicken in there instead. For a dairy-free version, skip the cheese and stir in the cumin along with a pinch of salt and pepper.
If your tortillas feel stiff or seem likely to crack when folded, lay them on a plate, cover with a damp towel, and microwave for about 30 seconds. This little bit of steam makes a huge difference in how easily they roll. Skipping this step is one of the most common reasons burritos split open during baking.
Lay a tortilla flat and spoon about a third of a cup of filling just below the center. Fold in both sides so they nearly meet, then bring up the bottom edge and roll it forward tightly, tucking the sides in as you go. Repeat with the remaining tortillas until your filling is used up.
Place the rolled burritos seam-side down, side by side, in your baking pan. Keeping them snug against each other actually helps them hold their shape while baking. If you're making both a chicken and a vegetarian batch, use two separate pans so you don't mix them up later.
Sprinkle the remaining shredded cheese over the top of the burritos and slide the pan into the oven. Bake for about 20 minutes, until everything is heated through, the cheese on top has melted, and the edges are just starting to turn golden. Let them sit for a couple of minutes before serving so the filling settles.