Melt 2 tablespoons butter in a large skillet over medium-low heat. Saute onions in butter until very soft and starting to brown, 15 to 20 minutes.
Melt 1 tablespoon butter in a second large skillet. Mash beans and add to skillet. (I use stainless steel pans, and I mashed the beans right in my skillet.) Add in half of the tomato sauce and the taco seasoning. Cook until heated through.
Mix the enchilada sauce with the remaining tomato sauce and spread about 1/2 cup in the bottom of a 9×13 pan.
Spread a large spoonful of the bean mixture on a tortilla. Top with onions and then sprinkle generously with shredded cheese. Roll up and place, seam side down, in the 9×13 pan. Repeat with the remaining tortillas.
Spread the remaining sauce over the enchiladas and top with additional cheese.