Prepare the pesto by combining basil, parmesan, lemon juice, garlic, and pine nuts in a food processor. Pulse until finely chopped, then gradually stream in olive oil while processing until smooth. Set aside.

Bring a large pot of salted water to a boil and add the pasta. Cook according to package directions until al dente. Reserve about 1/4 cup of pasta water before draining.

While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat.

Add the halved cherry tomatoes to the skillet and sprinkle with 1/4 teaspoon of salt. Cook for 2-4 minutes, or until the tomatoes begin to soften and release their juices.

Add the pesto and 2 tablespoons of reserved pasta water to the skillet. Stir to combine and heat through until just before boiling. If a saucier consistency is desired, add an additional tablespoon of pasta water.

Add the drained pasta to the skillet with the pesto mixture. Toss to coat the pasta evenly. Sprinkle with the remaining 1/4 teaspoon of salt.

Serve immediately, topped with additional grated parmesan cheese.