In a bowl, toss halved tomatoes and chopped basil with 1 tablespoon olive oil and a pinch of salt and pepper. Set aside to marinate while you prepare the pasta and sauce.
Add pasta to a large deep saucepan, cover with cold water, and add a generous pinch of salt. Set over high heat and bring to a boil, stirring occasionally. Cook pasta until noodles are al dente, about 7-9 minutes.
Meanwhile, while pasta is boiling, get all of the sauce ingredients ready to go, zesting and juicing lemons, etc.
When pasta is done, reserve ½ cup of pasta water and drain the noodles in a colander.
Working quickly while noodles are in the colander, add the lemon juice and zest, olive oil, heavy cream, and salt and pepper to the now empty pasta pot. Bring to a boil over medium high heat. Simmer for 1-2 minutes until slightly thickened, stirring often.
Add the drained pasta back to the pot along with the parmesan cheese and stir until coated. Add enough pasta water to make a loose sauce. Adjust seasonings as needed.
Stir in half of the marinated tomatoes to the pasta, and add rest of tomatoes to the top. Serve immediately.