Combine oil, garlic, chiles, and lime zest in a large shallow baking dish. Add steak and turn to coat. Cover and refrigerate for at least 4 hours or overnight. Preheat grill or grill pan over high heat. Remove steak from marinade, season with salt and pepper and grill for 2 to 3 minutes on either side until golden brown and cooked to medium-rare doneness. Let rest 5 minutes and slice on the bias into 1/2 inch thick slices. Preheat oven to 425 degrees F.
Place 8 tortillas on a flat work surface. Top each tortilla with 2 ounces of the cheddar. Divide the onions and steak over the cheese. Crumble 1 ounce of the blue cheese on top of the steak. Stack the tortillas to make 4 (2-layer) quesadillas and top each with the remaining tortillas. Brush the tops with olive oil and sprinkle with about 1/2 teaspoon of ancho chile powder. Carefully transfer the quesadillas to a baking sheet and bake in the oven until golden brown and the cheese has melted, about 5 to 7 minutes. Serve each with a large dollop of the Mushroom Relish on top and garnish with chopped cilantro and Roasted Red Pepper Sauce.
Wild Mushroom Relish:
For the grilled onions: Heat oil in a large saute pan over medium heat. Add the onions, season with salt and pepper and cook until soft and caramelized, about 25 to 30 minutes. For the wild mushroom relish: Heat oil in a large saute pan over high heat. Add the mushrooms and cook until golden brown. Add the garlic and cook for 1 minute. Add the wine and cook until completely reduced. Stir in the vinegar, thyme and parsley and season with salt and pepper, to taste.
Roasted Red Pepper Sauce:
Place peppers, onion, chipotle, lime juice and honey in a blender and blend until smooth. With the motor running, slowly add the oil and blend until emulsified. Season with salt and pepper, to taste.