Crumble the sausage meat and sauté without oil in a large skillet over medium-high heat until brown. Break it up with a fork if necessary. Remove with a slotted spoon and drain over paper towels on a plate.

Add the mushrooms to skillet and sauté until golden brown, about 8 minutes. Add the garlic and toss with a wooden spoon, then stir in the red peppers. Add salt and pepper to taste and stir in the thyme. Set aside.

In a medium-sized metal bowl, whisk 3 eggs and the rosemary. Season with salt and pepper. Heat one and a half teaspoons olive oil in a large nonstick skillet or omelet pan over medium heat. Add egg mixture to skillet. Cook until bottom of mixture is golden. Using the spatula, lift sides of omelet to let uncooked egg flow under, about 3 minutes. Arrange half of the sausage, mushrooms, peppers and cheese mixture over one side of the omelet and fold carefully to form a half-circle. Continue to cook for a few minutes until the omelet is lightly golden and completely set. Slide onto a serving plate and repeat with remaining eggs and filling. Garnish with fresh rosemary or thyme and serve warm.