Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Place garlic cloves in a single layer in a small baking dish. Add 1/2 cup olive oil to cover cloves, cover with foil, and bake 45 minutes, until golden brown and fork-tender. Meanwhile, in another baking dish, toss tomatoes with enough oil to coat. Lightly season with salt and pepper and roast at same temperature until tomatoes blister, about 25 minutes.
Strain garlic cloves and set aside in a small bowl, reserving infused oil separately. In a blender, add the roasted tomatoes, roasted garlic, Parmesan, and basil. Pulse until combined. While machine is running, drizzle in 1/2 cup olive oil until pesto comes together. Season with 1 1/2 teaspoons of salt. Remove to a bowl, cover with plastic wrap and reserve.
Bring a large pot of salted water to a boil over medium heat. Add the linguine and cook until al dente. Drain.
Meanwhile, heat a saute pan over medium-high heat. Add 2 tablespoons of the garlic oil. Season the shrimp with salt and pepper and saute until the shrimp turn pink and is cooked through.
In a large bowl add the linguine and some of the pesto. Toss to coat and top with the shrimp. Garnish with toasted pine nuts and serve.