Cook tortellini according to package directions. Drain and set aside.
Stir together cream, 1/2 teaspoon salt, and nutmeg in a saucepan over medium heat; bring to a boil, reduce heat, and cook 15 minutes or until cream has thickened and will coat back of spoon. Remove from heat, and set aside.
Melt butter in a large skillet over medium heat. Add shallots and garlic; cook, covered, 2 to 3 minutes, stirring occasionally. Increase heat to medium high; add mushrooms and remaining 1/2 teaspoon of salt. Cover and cook 8 minutes. Uncover and cook until liquid evaporates.
Add cream mixture, 1/3 cup grated Parmigiano-Reggiano cheese, and pepper to skillet; stir until blended.
Toss pasta with mushroom sauce.
Sprinkle with remaining 2/3 cup grated cheese. Serve pasta in warmed bowls. Garnish, if desired.