Warm olive oil in a large skillet over medium heat. Add zucchini and garlic to hot oil, and season with salt and red pepper flakes. Cook, turning occasionally, until zucchini are well browned on all sides, about 20 minutes.
Meanwhile, bring a large pot of generously salted water to boil. Add pasta, and cook until al dente, about 8 to 10 minutes. Drain, and set aside.
Stir milk into zucchini, and simmer until it is reduced by about half, about 10 minutes. Add pasta to skillet, and stir well. Sprinkle parsley and 1/4 cup Parmesan over the top, and toss. Garnish with remaining Parmesan to serve.