Combine mushrooms and boiling water in a small bowl; let stand 30 minutes. Drain, reserving liquid. Coarsely chop mushrooms; set aside.
Combine mushroom liquid and broth in a saucepan; place over medium heat. Cover and bring to a simmer; reduce heat to low, and keep warm. (Do not boil.)
Cut veal into 1 1/2-inch pieces. Combine veal and next 3 ingredients, tossing lightly. Coat a large nonstick skillet with cooking spray; add oil, and place over medium heat until hot. Add veal and garlic; cook 3 minutes or until browned, stirring occasionally. Remove from skillet, and keep warm.
Add rice and wine to skillet; cook, stirring constantly, 2 minutes. Reduce heat to medium-low.Add 1 cup simmering broth mixture to rice, stirring constantly until most of liquid is absorbed. Add remaining broth, 1/2 cup at a time, cooking and stirring constantly until each 1/2 cup addition is absorbed (about 40 minutes). (Rice will be tender and will have a creamy consistency.) Add mushrooms, veal, and peas; cook, stirring constantly, until mixture is thoroughly heated. Top with cheese.