01 - Bring a large pot of salted water to a rolling boil. Add the fettuccine or linguine and cook according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy pasta water. Drain the cooked pasta thoroughly.
02 - While the pasta is cooking, heat the olive oil in a large skillet over medium heat. Add the finely chopped shallot and minced garlic, sautéing until softened and fragrant, approximately 2 minutes.
03 - Add the cubed cooked beets to the skillet with the shallots and garlic, and sauté for another 2 minutes. Carefully transfer this mixture to a blender or food processor.
04 - Into the blender with the beet mixture, add the heavy cream, grated Parmesan cheese, fresh lemon juice, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and the optional pinch of nutmeg. Blend until the sauce is completely smooth and achieves a creamy consistency.
05 - Return the blended beet sauce to the skillet. Warm the sauce gently over low heat, stirring occasionally. If the sauce appears too thick, gradually add the reserved pasta water, a tablespoon at a time, until your desired consistency is reached.
06 - Add the drained pasta directly into the skillet with the warm beet sauce. Toss thoroughly until all strands of pasta are evenly coated and heated through.
07 - Portion the pink pasta into individual serving bowls. Garnish generously with additional grated Parmesan cheese, chopped fresh basil or parsley, and a sprinkle of freshly cracked black pepper before serving immediately.