Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, following the package instructions. Reserve about 1/2 cup of the pasta cooking water before draining.

Meanwhile, place the peeled and chopped beetroot in a saucepan with a little water, cover, and simmer until tender when pierced with a fork, about 13–15 minutes.

Heat the olive oil in a small pan over medium heat. Add the minced garlic and sauté briefly until fragrant but not browned.

Transfer the cooked beetroot, sautéed garlic, crumbled feta, lemon juice, and 2–3 tablespoons of the reserved pasta water into a blender or food processor.

Blend until smooth and creamy, adding more pasta water as needed to reach a sauce-like consistency.

Taste and adjust seasoning with salt and black pepper.

Toss the cooked pasta with the beet sauce until well coated.

Divide among plates and garnish with fresh basil or cilantro if you like.