Preheat oven to 375 degrees F.
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.
Note: There will be leftover pesto.