Preheat oven to 350 degrees. In a saucepan filled with 4 cups of boiling water, cook brown rice for about 20 minutes and drain. In a skillet, heat oil, melt butter, and saute vegetables for a few minutes. Add rice and remove from heat. Butter a baking dish and spoon in alternate layers of rice, crabmeat. Set aside.
In another bowl, pour béchamel sauce and season with salt, pepper, and thyme. Add 1/3 the amount of cheese and pour over the rice mixture. Sprinkle rest of cheese and breadcrumbs over mixture and bake for 30 minutes. Bake until cheese and breadcrumb layer is golden