Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
In a large skillet, heat 2 tablespoons of oil over medium-high heat. Add the turkey sausage and cook, stirring frequently, until cooked through, about 5 minutes. Add the garlic and cook for 1 minute. Remove the pan from the heat. Stir in the mascarpone cheese. Add the thyme, oregano, bread crumbs, 1/2 of the Gorgonzola, 1/2 teaspoon salt and 1/2 teaspoon pepper. Stir until all ingredients are combined.
Brush the mushrooms on both sides with the remaining oil and season with salt and pepper. Grill the mushrooms, stem side down, for 3 minutes. Turn the mushrooms over and grill for 2 minutes until tender. Fill each mushroom with the sausage mixture and top with the remaining Gorgonzola. Return the mushrooms to the grill and cook until the stuffing is warmed through and the cheese starts to melt, about 5 to 7 minutes.
Cook's Note: The assembled mushrooms can also be placed on a baking sheet and cooked under a preheated broiler until warmed through.