Look for: Tight, small heads without browning or bruising.
Prep: Snip off tough outer leaves; cut off top quarter and trim off woody stem.
Braise: Heat 2 teaspoons extra-virgin olive oil in a large skillet; add baby artichokes and cook for 1 minute, stirring constantly. Add 1 cup each white wine (or dry vermouth) and water and 1 teaspoon dried thyme (or rosemary or tarragon). Bring to a simmer; cover, reduce heat and cook until tender, about 15 minutes.
Grill: Halve artichokes, scoop out the choke if necessary, then toss with 1 tablespoon extra-virgin olive oil and 1/2 teaspoon kosher salt. Preheat grill. Place the artichokes over direct, medium-high heat and cook, turning once or twice, until tender, about 8 minutes.
Microwave: Place artichokes in a large glass pie pan or baking dish, add 1/2 cup white wine (or dry vermouth), 1/2 teaspoon salt and 1 teaspoon dried thyme. Cover tightly and microwave on High until tender, about 8 minutes.
Steam: Place artichokes in a steamer basket over 2 inches of water in a large pot set over high heat. Cover and steam until tender, about 15 minutes.