Cook rice according to package directions, omitting salt and fat.
While rice cooks, place flour in a small, heavy saucepan. Gradually add milk, stirring with a wire whisk. Cook over medium heat, stirring constantly, 8 minutes or until thickened and bubbly. Add cheese, stirring until cheese melts. Remove from heat, and stir in pimiento, salt, and pepper.
Combine cheese mixture, broccoli, and rice in a large bowl, stirring well. Spoon into a 1 1/2-quart casserole. Cover with heavy-duty plastic wrap, and vent. Microwave at HIGH 5 minutes. Let stand, covered, 10 minutes.