Preheat oven to 400F. Place each beet and garlic bulb on top of a tinfoil square. Drizzle olive oil, salt, and pepper then wrap in tinfoil. Add to a baking sheet then bake for 60 mins. Once complete, set aside to let cool.
Cook pasta as directed then strain the pasta water into bowl (you will use this in the beet sauce). Add strained pasta back to pot and set aside.
To remove the skin from the beets, run under cool water and use your thumbs to peel it back. Cut into cubes then set aside.
Add olive oil, lemon juice, feta (save some for serving), cleaned beets, garlic cloves, 1/4 cup pasta water, salt, and pepper. Blend until smooth. Taste as you go to adjust seasoning or add in more pasta water to reach desired sauce consistency.
Pour sauce over the pasta in the pot. Stir to combine and coat noodles well. Divide pasta into serving bowls then top with chopped walnuts, fresh basil, and vegan feta.