Black Bean Smash Burger

Name: Black Bean Smash Burger
Ingredients: ½ cup mayonnaise; 2 Tbsp. adobo sauce from a can of chipotle chiles in adobo; 2 Tbsp. (or more) vegetable oil, divided; 1 medium red onion, finely chopped; 1½ tsp. Diamond Crystal or ¾ tsp. Morton kosher salt, divided, plus more; 3 garlic cloves, finely chopped; 1 tsp. ground cumin; ½ tsp. ground coriander; 1 8-oz. block pepper Jack cheese, divided; 1 15-oz. can black beans, rinsed; 1 large egg, beaten to blend; 2 chipotle chiles in adobo, chopped; ½ cup plain dried breadcrumbs; 4 brioche buns, split; Unsalted butter, room temperature (for buns); Shredded iceberg lettuce, sliced red onion, and sliced heirloom or beefsteak tomato (for serving)