Preheat oven to 400°F. Place tomatoes on a baking sheet. Drizzle with 1T of oil and season with sugar and salt. Toss to coat. Roast for 6-10 minutes or until tomatoes are blistered and starting to burst, rotating pan half way through. If needed, take some tomatoes out earlier than others (as they are cooked), checking every few minutes.
While tomatoes are roasting, bring a large pot of salted water to a boil. Add pasta and cook until al dente, stirring occasionally. Drain, reserving a cup of pasta water, and set aside.
While the tomatoes and pasta are cooking, combine nuts and garlic in a food processor or good quality blender, and pulse until finely ground. Add basil, season lightly with salt and drizzle in a small amount of the remaining oil. Process until finely chopped, but do not over-process. Stream in olive oil slowly while blending until a thick paste forms. Add cheese and pulse to combine. Stir in lemon juice. Taste and adjust seasoning, if needed.
Add hot pasta to a bowl with pesto a couple tablespoons of pasta water, as needed, and stir to combine. Top with roasted tomatoes. Enjoy.
*NOTE: To toast pine nuts, add them to a small, cold pan. Turn heat to medium. Toss frequently as nuts gently toast, for about 3-4 minutes or until fragrant and lightly golden. Do not brown.