Preheat oven to 375 degrees F. Line a large baking sheet with aluminum foil and spray with nonstick spray.

Wash your artichokes thoroughly, and scrub lightly with a vegetable brush if you have one.

Cut 1 inch off the top of each artichoke, and 1/2 inch off the bottom of the stem. Immediately rub the cut portions with half a lemon.

Trim the thorns from the very top of each leaf. It's okay to leave them if you want. They soften in the oven anyway.

Use a sharp serrated knife to cut each artichoke in half. Rub the cut side with the half lemon to prevent browning.

Use a sharp knife or a sturdy spoon to remove the "choke" from the center of each artichoke half. This includes all the fuzzy stuff and the purple leaves in the center. (see photos) Squeeze some juice from your lemon half into the center to prevent browning.

In a small bowl, melt 3 tablespoons of butter in the microwave. Add the minced garlic and the lemon juice.

Line up the artichoke halves cut side up on the prepared pan with foil.

Use a spoon to drizzle the butter mixture over the artichokes, making sure to get in the crevices.

Flip the artichokes over so that they are cut side down. Use your hands to rub some of the butter that has dripped off onto the uncut sides of the artichokes.

Roast the artichokes at 375 for about 40-48 minutes. Start checking at 40 minutes as the cook time will depend on the size of your artichokes.

Use a sharp knife and insert it into the bottom of the artichoke, next to the stem. If the knife slides in fairly easy, like a baked potato, then it is done. The bottom (cut) sides of the artichokes should be browned as well.

Take the pan out of the oven and use tongs to flip each artichoke over. Sprinkle each one with a little bit of Parmesan cheese.

Turn the oven to a broil. Move the oven rack to the top. Return the pan to the oven and broil for no more than 1 minute, checking frequently. Don't walk away! You just want to get the cheese melted and a little brown.

Remove from the oven and let cool slightly before moving to a plate to serve.

In a small bowl, stir together equal parts mayonnaise and pesto. (Or whatever ratio looks good to you.)

Serve the artichokes with the pesto sauce. Enjoy!