Garlic bread, for serving (optional but recommended!)
Preheat the oven to 425°F. Line a baking sheet with parchment paper. Place the tomatoes on the baking sheet, drizzle with about 1 tablespoon of the oil, and season well with salt, pepper, and a pinch of sugar.
Roast for 15-20 minutes or until the tomatoes are bursting and even charred in some spots. Set aside.
Meanwhile, bring a large pot of salted water to a boil. Cook the linguine until el dente and drain, reserving about 1 cup of the cooking liquid.
Heat a large skillet over medium-high heat and add the remaining oil and the butter. Pat the scallops dry with paper towels and then season with salt and pepper. Sear in the hot skillet for 1-2 minutes per side, leaving them undisturbed so that each side can caramelize and develop a golden brown crust. Remove from the pan and set aside.
Place the linguine in a large bowl with the pesto, half of the grated cheese, and roughly ¼ cup of the cooking liquid. Toss thoroughly with tongs so that each strand of pasta is well coated in the pesto and everything becomes sort of saucy. Add more cooking liquid, as needed, to thin out the pesto.
Divide the pasta among serving bowls and top with the roasted tomatoes, seared scallops, more cheese, and fresh basil. Serve immediately with lots of garlic bread on the side.