Cook pasta in salted boiling water until al dente according to package directions. Drain and set aside.
In a large skillet, heat olive oil or butter over medium heat. Add chopped onion and sauté until translucent, about 3-4 minutes.
Add minced garlic and cook for another minute until fragrant.
Add chopped beets to the pan, cover with broth or water, and bring to a simmer. Cook covered for 15-20 minutes until beets are tender.
Transfer the beet mixture to a blender and add heavy cream and Parmesan cheese. Blend until completely smooth.
Return the sauce to the skillet and heat over low heat. Season with salt, pepper, and optional lemon juice to taste.
Add the cooked pasta to the sauce and toss until evenly coated.
Serve immediately, garnished with additional Parmesan if desired.