Melt butter in a skillet over medium heat. Cook onion and poblano pepper until softened, about 5 minutes. Transfer mixture to a plate. Add ground beef and chorizo to the skillet. Cook, stirring often to break up meat, until browned and crumbly, 5 to 7 minutes. Add enchilada seasoning and tomato powder. Add water, ketchup, and Worcestershire sauce. Return cooked onion mixture to the skillet. Simmer until flavors combine, about 5 minutes more.

Serve meat mixture on toasted buns topped with Oaxaca cheese and avocado.