Trim stalks flush with fennel bulb and cut each bulb lengthwise into quarters, or halves, if using small bulbs.
In a heavy saucepan large enough to hold the fennel flat in one layer, melt 1 tablespoon butter over moderate heat. Add fennel garlic, thyme, and toss to coat with butter. Season with salt and pepper, to taste. Add wine, if using, and chicken stock. Bring mixture to a boil, reduce heat to a simmer and cover. Braise for 15 to 20 minutes, or until vegetables are tender. Stir in remaining tablespoon butter and salt and pepper, to taste.