In a large bowl, toss together shrimp, oil, salt and pepper. Set aside.

In a mortar and pestle, or a food processor, mash your basil leaves and garlic with salt and pepper until a paste forms. Fold in your butter until completely combined. Set aside.

Heat your grill over medium-high heat. Place your shrimp and lemon halves on the grill, and cook your shrimp for about 2 to 3 minutes per side. Your shrimp shells should turn a nice orange-pink color. Transfer to a cast iron skillet on the grill.

Then add in your compound butter, and toss to combine with your shell on shrimp. Finish with a big squeeze of lemon juice, and serve alongside an empty bowl to add in your shrimp shells as you peel and eat.