How to Make It
Preheat the oven to 475°. Season the capon cavities with salt and pepper and stuff each with 2 sprigs each of thyme and rosemary and 4 tablespoons of butter. Tie the legs of each capon together with kitchen string. Season the outside of the capons with salt and pepper; fold the wing tips under. Place each capon in a separate roasting pan (the 2 pans should fit on the same oven shelf).
Add 1 cup of stock to each pan and roast the capons for 20 minutes. Baste the capons and arrange 2 halved heads of garlic in each pan, cut side down. Lower the oven temperature to 350° and roast the capons for another 20 minutes. If making Glazed Caramelized Carrots, remove 1/4 cup of pan drippings from each pan, using a bulb baster, and reserve. Continue to roast the capons for about 1 hour longer, basting 2 more times, until an instant-read thermometer inserted into the inner thigh registers 170°.
Lift the capons from the roasting pan, tilting them to allow the cavity juices to run into the pan. Transfer the capons to a carving board and cover loosely with foil. Set the garlic halves aside. Strain the pan juices into a large glass measuring cup. Skim 1 1/2 tablespoons of fat from the surface; transfer the fat to a small bowl. Skim off and discard the remaining fat. Whisk the flour into the reserved fat to make a paste. Set each roasting pan over moderate heat and when sizzling, pour 1 cup of the remaining stock into each pan. Simmer the stock, scraping up any browned bits from the bottom and sides of the pans, about 4 minutes. Add the stock to the pan juices.
Transfer the juices to a medium saucepan. Squeeze the softened garlic cloves into the pan juices and bring to a simmer over moderate heat. With an immersion blender, puree the garlic until the sauce is slightly thickened. Whisk about 1/2 cup of the gravy into the flour paste until smooth, then whisk it back into the saucepan and bring to a boil. Simmer over low heat, whisking occasionally, until no floury taste remains, about 5 minutes. Season the gravy with salt and pepper.
Carve the capons and serve, passing the gravy at the table.