Bring a large pot of heavily salted water to a rolling boil. Add the linguine and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.
While the pasta cooks, melt the butter in a large skillet over medium heat. Add the minced garlic and red pepper flakes (if using) and cook, stirring constantly, for 1 minute until fragrant and just beginning to turn golden.
Add the halved cherry tomatoes to the skillet with a pinch of salt. Cook, stirring occasionally, for 3-4 minutes until the tomatoes soften and begin to release their juices.
Add the spinach in handfuls, stirring gently until it wilts, about 1-2 minutes. Remove the skillet from the heat immediately once wilted.
Add the drained pasta to the skillet along with the lemon zest, lemon juice, and half of the Parmesan. Toss well with tongs, adding a splash of reserved pasta water as needed to create a light, glossy sauce that coats the pasta. Season with salt and black pepper to taste.
Divide among bowls, top with remaining Parmesan, torn basil leaves, and an extra crack of black pepper. Serve immediately.