Prep the artichoke by cutting the top 1 inch of the artichoke and then clipping the pointed tips of the leaves. Gently scrape out the leaves in the center of the artichoke as well as the fuzzy "choke". Rinse the artichoke under cool water. Press the garlic cloves inside the center of artichoke, drizzle lightly with 1 teaspoon olive oil.
Combine the remaining olive oil, salt and lemon juice together in a bowl. Rub over the artichoke, making sure to get the areas where you cut to keep them from turning brown. Bake in the preheated oven for 1 hour and 20 minutes or until the artichoke is tender and the leaves pull away easily.
Remove the garlic cloves from the center and mash together in a bowl. Add in mayonnaise, lemon juice and lemon zest. Season to taste with salt and pepper. Serve with artichoke.