Simple seasonings and lemon make these vegetables an ideal accompaniment to any main dish.
Preheat oven to 425 degrees. Place a saucepan of water over high heat. Add the juice of 1 lemon, add the squeezed halves, and bring to a boil. Fill a medium bowl with water; squeeze juice of remaining 2 lemons into water. Add squeezed lemon halves. Cut tops off artichokes; remove tough outer leaves. Trim stems; pare down to pale-green heart. Cut in half; add to acidulated water.
Drain artichokes, add to boiling water, and cook 3 minutes. Drain; set aside.
Place potatoes in a large bowl with oil, rosemary, salt, and pepper; toss to coat. Add artichokes. Spread onto two 12-by-18-inch pans; do not overcrowd the pans or potatoes will steam instead of roast. Place in oven until tender and browned, 45 to 55 minutes. Rotate pans once to ensure even cooking. Remove from oven; serve.