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.
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.
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.