Make the Aioli:

Place the garlic, salt, egg yolks, and lemon juice and zest in a food processor or blender and process until smooth. Slowly add the oil, drop by drop at first, until thickened. Season with salt and white pepper to taste. Refrigerate until ready to use.

Prepare the Shrimp:

Whisk oil and garlic in small bowl to blend.

Drain the shrimp, rinse, and drain well. Using kitchen scissors, cut shells down center of back side and devein, leaving shells intact.

Grill shrimp in shells until charred and just opaque, 3 to 4 minutes per side.

Grill bread until beginning to brown, about 2 minutes per side. Transfer shrimp to another large bowl. Add half of garlic oil and toss to coat. Mound shrimp on platter. Serve with grilled bread and remaining garlic oil.