Heat oil in a large pan. Slice mushrooms into 1/4-inch strips. Set aside.
Add onions to pan and cook 5 minutes, until softened. Add garlic and cook 30 seconds.
Add tempeh, mushroom slices, chili powder, and cumin. Cook 10 minutes.
Stir in lime juice, tomato paste, cilantro, salt, and cayenne pepper. Cook 5 minutes.
Toast tortillas in a small dry pan, 30 seconds on each side. Transfer to a serving platter and cover with a clean dish towel to keep warm.
Assemble each taco by placing 1/4 cup of filling in a tortilla. Top with avocados, radishes, and Charred Tomato Salsa.