1. Rinse and drain fresh artichokes. Trim leaves off just above artichoke bottoms. Discard leaves or save to cook separately.
2. In a 3- to 4-quart pan over high heat, bring 1 1/2 quarts water, thyme, coriander, basil, and peppercorns to a boil. Add fresh artichoke bottoms, cover, reduce heat, and simmer until bottoms are tender when pierced, about 30 minutes. (Or add frozen artichoke hearts and simmer until thawed and seasoned, about 10 minutes.) Drain artichokes. Trim coarse fibers from artichoke bottoms, break off remaining leaves, and scoop out and discard fuzzy centers.
3. Place artichokes in a shallow 8- or 9-inch-wide casserole; turn bottoms cup side up. Cover artichokes with spinach filling and sprinkle with cheese.
4. Bake in a 350° oven until cheese is lightly browned, about 35 minutes (45 minutes if chilled).