Combine boiling water and mushrooms; let stand 10 minutes or until soft. Drain through a colander over a bowl. Reserve 1 1/4 cups soaking liquid, and chop mushrooms.
Bring soaking liquid and broth to a simmer in a small saucepan (do not boil). Keep broth mixture warm over low heat.
Heat a large saucepan over medium-high heat. Coat pan with cooking spray. Add rice, shallots, and garlic; sauté 5 minutes. Add wine, and 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, cheeses, thyme, salt, and pepper; stir gently just until the cheese melts. Serve warm.