1. In a 12- by 18-inch baking pan, mix artichokes with 2 tablespoons oil, the salt, and the pepper to coat.
2. Bake in a 450° oven, stirring occasionally, until artichokes are browned and crisp at the edges and tender when pierced, about 15 minutes.
3. Spoon artichokes into a bowl and add lemon juice, mint, and remaining 1 tablespoon oil; mix thoroughly. Using a vegetable peeler, shave parmesan cheese over salad. Serve warm.
Trimming baby artichokes:
1. Cut off the stem at the base of the artichoke, using a sharp knife.
2. Peel back and snap off the leaves all around the base of the artichoke until you reach the tender layer of leaves that are yellow at the bottom and green at the top.
3. Cut off the top third of the remaining leaves (the green part). With a sharp paring knife, trim off all of the remaining green, fibrous material from around the base of the artichoke.