Increase heat to high; bring to a boil. Reduce heat, and simmer 30 minutes.
Stir in brown rice; cover and simmer 30 minutes. Remove from heat.
Preheat oven to 400°.
Heat remaining 2 tablespoons butter over high heat in a large skillet; swirl to coat. Add celery and remaining 1/2 teaspoon salt; saute 1 minute. Reduce heat to medium; cook 4 minutes, stirring occasionally.
Remove from heat.
Combine rice mixture, celery mixture, cherries, and onions in a large bowl. Spoon stuffing into chicken breast and fold each breast. Cover with foil. Bake at 400° for 30 minutes.
While baking prepare gravy.
Pour fat from drippings into a bowl and reserve. Whisk flour into remaining drippings left in pan; mixture will seem dry. Add 2 tablespoons reserved fat, or as needed, to the drippings mixture to combine with flour.
Place pan of drippings mixture over low heat and toast flour until light brown and mixture gives off a nutty fragrance, about 5 minutes.
Drizzle about 1/3 cup cold chicken stock at a time into pan drippings, whisking each addition of stock into mixture until thoroughly combined. Continue whisking, scraping any browned pan drippings from the bottom of the pan into gravy; bring to a simmer. Continue to cook, whisking constantly, until gravy is thick and flour has combined with the liquid, 8 to 10 minutes.
Adjust thickness of gravy; if too thick, whisk in a little more stock. If gravy is too thin, continue to simmer, whisking constantly, until reduced and thickened, about 10 more minutes. For the smoothest texture, strain gravy before serving.
Spoon gravy over top of chicken. Serve with mashed potatoes and veggie of choice.