Cook the rice according to package directions, omitting salt, fat, and seasoning packet.
Preheat oven to 400°.
Lightly spoon flour into a dry measuring cup; level with a knife. Place flour in a medium saucepan. Gradually add milk, stirring constantly with a whisk until blended. Cook over medium heat until thick (about 8 minutes), stirring constantly. Remove from heat. Add 3/4 cup fontina, 3/4 cup Parmesan, thyme, salt, and pepper; stir until cheese melts. Stir in rice, asparagus, peas, and onions. Spoon rice mixture into a 13 x 9–inch baking dish coated with cooking spray. Sprinkle evenly with 1/4 cup fontina and 1/4 cup Parmesan. Bake at 400° for 18 minutes or until bubbly.