Preheat oven to 425°F. Line a baking dish with parchment paper. Toss together beets, onion, garlic, oil, thyme, salt, and pepper. Cover with foil. Roast for 40 to 45 minutes until beets are tender.
12 ounces beets, 1 sweet onion, 4 garlic cloves, 2 Tablespoons olive oil, 1 teaspoon chopped fresh thyme, 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper
While the beets are roasting, cook pasta in salted water according to package directions until al dente. Reserve 1 cup of the starchy pasta water before draining and set aside. Drain pasta and return to the pot.
1 (16-ounce) package fettuccine
When the beets are fork tender, transfer the roasted vegetables to a blender or food processor along with 1/2 cup of reserved pasta water. Pulse until the vegetables start to break down, then increase the speed and puree until smooth.
Combine the beet pasta sauce with the cooked pasta and toss well to coat. Stir in Parmesan cheese and red bell pepper flakes. Add more of the reserved pasta water as needed until the pasta is evenly coated and the sauce is silky, not gummy or thick.
1/2 cup shredded Parmesan cheese, 1/2 teaspoon red pepper flakes
Divide the pasta between pasta bowls or plates and dot with chunks of goat cheese. Garnish with a generous amount of chopped pistachios and torn basil leaves. Sprinkle with additional red pepper flakes, to taste.
4 ounces plain goat cheese, 1/2 to 3/4 cup roasted & salted pistachios, 2 Tablespoons torn fresh basil