Heat the oven to 375F.
Thoroughly wash your artichokes. Using a sharp knife, cut the bottom half-inch of the artichoke stem and top 1 inch of the artichoke. Trim the pointed tip of every leaf around the artichoke and pull off any small leaves towards the branch.
Slice the artichoke in half vertically. Use a spoon to remove the fuzzy center of the artichoke. Then rub lemon juice all over the artichoke to prevent browning. Repeat to all artichokes.
Place the artichoke halves in a baking dish, cut side up. Drizzle with olive oil and cover with lemon slices and garlic cloves. Generously sprinkle in salt and pepper. Then flip the artichokes to be cut side down.
Cover the baking dish in foil and bake for 1 hour.
While the artichokes bake, prepare the pesto aioli. In a food processor, combine garlic, basil, freshly grated parmesan cheese, lemon juice, olive oil, salt, pepper, and mayonnaise. Scoop into a small bowl and set aside.
Remove the artichokes from the oven. Turn them to be cut side up and bake for 5 more minutes until golden brown and crisp.
Spoon the garlic lemon olive oil over the artichokes for some added flavor. Serve warm alongside the pesto aioli.