Bring a large pot of well-salted water to a rolling boil. Cook pasta until just shy of al dente, 1 minute less than package directions. Reserve 1 cup pasta water, then drain.
Heat olive oil in a large deep skillet over medium-high heat. Add cherry tomatoes and a pinch of salt. Cook undisturbed 2 minutes, then stir and cook 4–5 minutes more, until skins split and tomatoes collapse into a jammy sauce.
Reduce heat to low. Stir in the pesto for 30 seconds to loosen in the warm oil. Do not boil.
Add drained pasta to the skillet. Toss with tongs, adding reserved pasta water a splash at a time, until glossy and well coated.
Remove from heat. Add Parmesan and toss. Season with salt and black pepper. Serve immediately with extra Parmesan.