Heat a large saucepan over medium-high heat. Coat pan with cooking spray. Add rice, shallots, and garlic to pan; sauté 5 minutes. Add wine; cook until liquid evaporates (about 2 minutes).
Add 1 cup broth mixture to rice mixture; cook over medium heat 5 minutes or until the liquid is nearly absorbed, stirring occasionally. Add remaining broth mixture, 1/2 cup at a time, stirring occasionally until each portion of broth mixture is absorbed before adding the next (about 25 minutes total). Add mushrooms, Parmigiano-Reggiano and mascarpone cheeses, thyme, salt, and pepper; stir gently just until cheeses melt. Serve warm.
Arrange asparagus evenly on a lightly greased 15- x 10-inch jelly-roll pan. Drizzle with olive oil, and sprinkle with salt and pepper; toss to coat.
Melt butter in a large skillet over medium heat. Cook, stirring occasionally, 4 minutes or until butter is lightly browned. Remove from heat; stir in soy sauce and balsamic vinegar. Drizzle over asparagus, tossing to coat. Serve immediately.