Preheat oven to 350°F and lightly grease a large roasting pan with one tablespoon olive oil. Set aside.
Heat remaining olive oil in a large skillet over medium heat. Add diced Poblano peppers and cook, stirring occasionally, until the peppers soften and develop a bit of color, approximately 3-4 minutes.
Add turkey sausage to the skillet. Cook until no longer pink, approximately 6-8 minutes, breaking up the sausage into small pieces while cooking.
Add goat cheese to skillet and cover for 1-2 minutes. Remove cover and stir until cheese is completely melted and combined with the turkey and pepper mixture. Remove from heat and set aside.
Fill each mushroom cap with some of the turkey mixture. Drizzle the mushrooms with remaining olive oil and season with salt and black pepper, as desired.
Place pan in the pre-heated oven and roast until the mushrooms are slightly browned around the edges, approximately 10-12 minutes. Remove from oven and serve immediately. Enjoy!