Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray.
Add garlic and turkey to pan; cook 5 minutes or until turkey is no longer pink, stirring to crumble.
Add crushed red and ground red peppers; cook 1 minute. Spoon turkey mixture into a bowl.
Recoat pan with cooking spray; return pan to medium-high heat.
Add 1/2 teaspoon salt and mushrooms to pan; saut 5 minutes. Stir in peas; cook 1 minute. Stir in turkey mixture; cook 3 minutes or until thoroughly heated. Cover and set aside.
Bring a large saucepan of water to a boil.
Add gnocchi to pan; cook just until gnocchi begin to float.
Drain gnocchi, reserving 1/2 cup cooking liquid.
Combine turkey mixture, remaining 1/4 teaspoon salt, 1/2 cup cooking liquid, and gnocchi in a large bowl; toss well.