Bring salted water in a large pot to a boil. Cook orecchiette according to package instructions until al dente. Reserve 1⁄2 cup pasta water.
Meanwhile, heat olive oil in a large skillet over medium heat. Once hot, add squash and season with salt. Cook until tender, about 5 minutes. Transfer to a plate.
In the same skillet, melt butter over medium heat. Add garlic and chile flakes, cooking until fragrant, about 30 seconds. Add milk and summer savory and bring to a gentle simmer. Add brie and stir until smooth. Toss cooked pasta and sautéed squash into the sauce, adding reserved pasta water to thin the sauce as desired. Serve immediately.