Wash, peel, and chop the beets. Heat 1 tablespoon of olive oil in a medium pan and sauté minced garlic until fragrant, about 1-2 minutes. Add chopped beets, season with salt, and add a splash of water. Cover and cook for 13-15 minutes until tender.

Bring a large pot of salted water to a boil. Add pasta and cook according to package instructions until al dente, typically around 8-10 minutes. Reserve 1/2 cup of pasta water, drain the pasta.

In a high-speed blender, combine cooked beets, sautéed garlic, crumbled feta, and lemon juice. Blend with reserved pasta water until smooth and velvety.

Return the drained pasta to the pot over low heat and pour the beetroot sauce over it. Mix gently until pasta is coated, adding more pasta water if needed.

Plate the pasta and serve immediately, garnished with extra feta and herbs if desired.