Toast pine nuts in a dry skillet over medium heat until golden, about 3 minutes; set aside, reserving a spoonful for garnish.

Cook spaghetti in salted boiling water until just shy of al dente; reserve 1 cup pasta water before draining.

In a food processor, pulse spinach, basil, garlic, toasted pine nuts, and Parmesan until finely chopped; stream in olive oil and blend until combined; season with salt and pepper.

In the same skillet over medium-high heat, sear halved cherry tomatoes cut-side down until charred and bursting, 3–4 minutes.

Add drained spaghetti to the skillet, spoon in pesto, toss with ¼ cup pasta water until glossy, adding more as needed. Serve hot with reserved pine nuts and extra Parmesan.