Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve a few tablespoons of pasta water if desired.
While the pasta cooks, heat a skillet over medium-low heat. Add the pine nuts and toast, stirring frequently, for 5–6 minutes until golden and fragrant. Remove immediately and set aside.
In a large skillet over medium heat, melt the butter. Whisk continuously until it turns golden brown and develops nutty brown bits on the bottom.
Add the minced garlic, zucchini, and summer squash. Toss well to coat in the brown butter.
Cook for about 5 minutes, stirring occasionally, until the squash becomes tender but still slightly firm.
Season with kosher salt and freshly cracked black pepper.
Drain the pasta and add it directly to the skillet. Reduce the heat to low.
Toss everything together until the pasta is coated in the brown butter sauce.
Add the crumbled goat cheese and gently toss until slightly melted and evenly distributed.
Stir in the toasted pine nuts and fresh basil leaves.
Serve the Summer Squash Pasta immediately with extra black pepper on top if desired.