Method:
Melt butter in a large skillet over medium high heat. Add chile powder, cumin and garlic and cook, stirring constantly, until fragrant, about 1 minute. Add mushrooms, onions and salt and cook until mushrooms are just tender, 8 to 10 minutes. Add tempeh and cook 2 minutes more, or until heated through. Remove skillet from heat. Add cilantro and toss to coat. Set aside to let cool, about 10 minutes.
Preheat grill to 350°F (a medium fire). Lightly brush 6 of the tortillas on one side with oil. Place tortillas, oil side down, on a large nonstick baking sheet. Divide mushroom mixture equally among the tortillas and top with cheese, distributing to equal thickness. Top with remaining 6 tortillas, and brush tops with oil.
Gently slide quesadillas onto the grill and cook for about 3 minutes on each side, until heated through and golden brown. Remove from the grill, set aside to let stand for 2 minutes, cut into wedges and serve.