1. Bring broth to a simmer in a medium saucepan; keep warm over low heat.
2. Melt butter in a large skillet over medium heat. Add onion; cook 2 minutes. Add 1 teaspoon garlic; cook 30 seconds, stirring constantly. Add rice; cook 1 minute, stirring constantly. Add wine; cook 2 minutes or until liquid is absorbed, stirring frequently. Stir in 1/2 cup broth; cook 2 minutes or until liquid is absorbed, stirring constantly. Add remaining broth, 1/2 cup at a time, stirring constantly until each portion of broth is absorbed before adding the next (about 20 minutes).
3. Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms to pan; sauté 5 minutes or until tender. Add remaining 1/2 teaspoon garlic and 1 teaspoon thyme; sauté 1 minute. Set aside.
4. Stir mushrooms, remaining 1 teaspoon thyme, peas, 1/4 cup cheese, and pepper into risotto; cook 3 minutes. Spoon about 1 1/4 cups risotto into each of 4 bowls; sprinkle each with 1 1/2 teaspoons cheese.