Preheat the oven to 350 degrees F (175 degrees C).

Heat oil in a medium skillet. Cook and stir onion and garlic in hot oil until onion is soft. Mash beans into onion mixture. Gradually stir in water; heat until warm, 2 to 3 minutes. Remove from heat and stir in soy sauce, chili powder, mustard, cumin, and cayenne pepper.

Divide bean mixture and mashed sweet potatoes evenly between warm tortillas; top with cheese. Fold tortillas, burrito-style, around fillings and place on a baking sheet.

Bake in the preheated oven until warmed through, about 12 minutes.