Meanwhile, bring a large pot of water to a boil. Place the artichokes into the boiling water, and season with salt and pepper. Throw in half of the garlic, and half of the shallot. Boil for about 30 minutes, or until a fork is easily inserted into the stem of the artichokes. Drain and set aside.
Melt the butter in a small pan over medium heat, and stir in the remaining garlic and shallot. Cook just until fragrant, then remove from the heat.
Place the artichoke halves onto the preheated grill. Brush some of the melted butter onto them. Cook for 5 to 10 minutes, brushing with butter occasionally, until lightly toasted. Serve with remaining butter as a dipping sauce.