Toss the squash with salt in a colander and let it drain for 30 minutes to remove excess moisture. Pat the squash dry with paper towels and carefully wipe away any residual salt grains.

Heat a portion of the oil in a 12-inch nonstick skillet over high heat until just smoking. Add half of the squash and cook, stirring occasionally, until golden brown and slightly charred, about 5 to 7 minutes; reduce the heat if the skillet begins to scorch. Transfer to a large plate and repeat the process with more oil and the remaining squash.

Heat more oil in the empty skillet over medium heat until shimmering. Add the onion and cook until softened and lightly browned, about 5 to 7 minutes.

Stir in the garlic, lemon zest, and pepper, and cook until fragrant. Add the cooked squash back into the skillet and cook until heated through.

Bring a large pot of salted water to a boil. Add the pasta and cook, stirring often, until al dente. Reserve 1/2 cup of the cooking water, then drain the pasta and return it to the pot.

Add the squash mixture, lemon juice, tomatoes, olives, mint, vinegar, and the remaining oil to the pot with the pasta and toss to combine. Season with salt and pepper to taste, adding the reserved cooking water as needed to loosen the consistency.

Serve immediately, sprinkling individual portions with the crumbled feta.