How to Make It
In a large pot of salted boiling water, cook the pasta until just al dente. Transfer 1 1/2 cups of the pasta cooking water to a small bowl and stir in the goat cheese until smooth. Drain the pasta.
Meanwhile, in a large, deep skillet, cook the stick of butter over moderately high heat until it turns brown and smells like roasted nuts, about 5 minutes. Add the garlic and cook, stirring, until lightly browned. Add the squash, season with salt and pepper and cook, stirring occasionally, for 1 minute, until just tender.
Add the pasta, goat cheese sauce, mint and the remaining 2 tablespoons of butter to the skillet. Reduce the heat to moderately low and cook, stirring, for 1 minute. Season with salt and pepper and transfer to a bowl. Drizzle with the olive oil and serve.