Trim 2 medium yellow squash and thinly slice crosswise into 1/4-inch rounds (about 4 cups). Finely chop 2 garlic cloves. Thinly slice 1 medium scallion crosswise (about 2 tablespoons). Juice 1/2 medium lemon until you have 1 tablespoon.
Place 2 tablespoons pine nuts in a large frying pan. Cook over medium heat, stirring occasionally, until toasted and light golden-brown, about 5 minutes. Transfer to a small bowl.
Melt 1 tablespoon unsalted butter and 1 tablespoon olive oil in the same pan over medium-high heat. Add the squash in an even layer and season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Cook, stirring every few minutes, until the squash is tender and light golden-brown, 8 to 10 minutes.
Push the squash to one side of the pan. Add the garlic and a pinch of red pepper flakes to the other side and cook, stirring often, until the garlic is light golden-brown and fragrant, about 1 minute. Toss with the squash and remove the pan from the heat. Add the pine nuts, scallion, and lemon juice, and toss to combine.
Transfer to a serving bowl. Tear 5 large fresh basil leaves into bite-sized pieces and scatter over the squash. Using a vegetable peeler, shave about 2 tablespoons Parmesan cheese over the squash.