In a large pot of boiling salted water, cook spaghetti until 1 minute shy of the package directions. Meanwhile, remove 3 tbsp. zest and squeeze 2 tbsp. juice from lemons. Reserve about 1 mug of the pasta cooking water; drain pasta. In a large saucepan, melt butter over medium. Add 1 1/2 cups of the Parmesan and the reserved cooking water. Add the hot pasta, lemon zest, and lemon juice. Toss until coated; season with kosher salt and pepper. Top with basil and the remaining 1/2 cup Parmesan.