Preheat grill or grill pan. Brush the mushrooms with 1/4 cup of the olive oil and season with salt and pepper to taste. Grill the mushrooms until golden brown and cooked through, remove from grill and coarsely chop. Preheat the oven to 450 degrees F. Place 8 tortillas on an ungreased baking sheet. Spread some of the roasted garlic puree on each. Divide the cheese among the tortillas, then the mushrooms and thyme and season to taste with salt and pepper. Stack to make 4 (2 layer) tortillas and cover with remaining tortilla, brush the tops with olive oil. Place on a lightly oiled baking sheet and bake or until the tortillas are lightly golden brown and the cheese has melted, about 5 to 7 minutes. Remove and drizzle with white truffle oil.