Toss the squash with salt in a colander set over a bowl. Let it sit for 20 minutes to release its liquid; the squash should feel slightly softened.

Spread the squash onto paper towels and pat dry. Removing the surface moisture and excess salt is key to achieving a proper sear later.

Bring a large pot of salted water to a boil. Cook the farfalle until al dente, then reserve 1/2 cup of the pasta cooking water before draining the pasta and returning it to the pot.

Heat 2 tablespoons of oil in a large skillet over medium-high heat until the oil shimmers. Add the shallots and cook until softened and translucent.

Increase the heat to high and add 2 more tablespoons of oil. Add the squash in an even layer and cook, stirring occasionally, until the edges are golden brown and tender.

Stir in the tomatoes, capers, lemon zest, and pepper. Cook until the tomatoes just begin to soften and release their juice.

Transfer the squash mixture to the pot with the cooked pasta. Add the remaining tablespoon of oil, lemon juice, parsley, and half of the goat cheese.

Toss the pasta vigorously, adding the reserved cooking water a little at a time until the cheese melts into a light, creamy sauce that coats every piece.

Serve immediately, topped with the remaining crumbled goat cheese.