Begin boiling the noodles in a pot. If you have a steamer to place on top of the pot, place it, pour in the frozen broccoli, and begin steaming the broccoli. If not, steam the broccoli in another pan by adding a half inch of water to the bottom of the pan and bringing to a boil. Pour in the broccoli and cover for 5-10 minutes until fork-tender. Alternatively, if you have fresh broccoli, place it on a baking sheet, drizzle with olive oil, salt, and pepper and bake at 400F for 20 minutes.
While the noodles are cooking, begin the alfredo sauce. In a large saucepan, melt the butter and sauté the garlic for 1-2 minutes. Whisk in the flour and slowly add in the whipping cream and milk and whisk until smooth. Bring the sauce to a boil over medium heat until thickened. Remove from heat and add in the nutmeg and parmesan. Stir until almost all the parmesan is melted (it will all melt later when the hot noodles are added). Add in the canned butternut squash and stir together. Season with salt and pepper to taste.
Once the noodles are done, reserve 1/2 cup of the pasta water and drain the noodles. Add the noodles to the butternut sauce along with the pasta water and stir until creamy and coated. Add in the broccoli.