Toss the squash with salt in a colander and let it sit over a bowl for 20 minutes to draw out excess moisture.

Toast the pine nuts in a large skillet over medium heat, shaking the pan frequently, until they are golden brown and fragrant. Transfer them to a small bowl immediately to stop the cooking.

Bring a large pot of salted water to a boil and cook the farfalle until al dente. Reserve 1/2 cup of the pasta cooking water before draining the noodles.

Pat the squash thoroughly dry with paper towels while the pasta cooks. The drier the squash, the better it will brown.

Heat half of the olive oil in the now-empty skillet over medium-high heat until it shimmers. Add the squash in a single layer and cook without stirring until the bottoms are deeply browned, about 4 to 5 minutes.

Stir the squash and continue to cook until it is tender and browned on the second side. Stir in the garlic and cook until fragrant, about 30 seconds.

Add the cherry tomatoes and cook just until they begin to soften and release their juices, about 2 minutes.

Add the cooked pasta, toasted pine nuts, basil, pepper, and the remaining olive oil to the skillet. Toss to combine, adding the reserved pasta water as needed to create a light sauce that coats the noodles.

Serve immediately with a dusting of Parmesan cheese while the basil is still vibrant.