Preheat oven to 350 degrees F (175 degrees C). Grease a 2 1/2-quart casserole dish.
Spread the rice into the bottom of the prepared casserole dish.
Melt butter in a saucepan over medium heat. Cook and stir flour in melted butter until frothy, 2 to 3 minutes; add half-and-half, chicken broth, rosemary, and salt to the saucepan. Stirring continually, cook the broth mixture until slightly thickened, about 5 minutes. Stir cooked chicken, mushrooms, bell pepper, and pimentos into the sauce; cook until the chicken is hot, 2 to 3 minutes. Pour the chicken mixture over the rice; stir lightly.
Bake in preheated oven until heated through and the rice is very tender, about 30 minutes.