1. Bring a large pot of cold water to a boil over high heat and salt it generously. Add the spaghetti and boil, stirring occasionally, until al dente, about 9 minutes. Drain, reserving about 1/2 cup of the cooking water.
2. Meanwhile, cut the beet green stems into 2-inch pieces. Cut the larger leaves into wide ribbons; leave the smaller ones whole. Swish the stems and then the leaves in a big bowl of cold water to clean (in batches if necessary); lift them from the bowl with your fingers, shake them off and blot with a paper towel-they don't have to be really dry.
3. Put the olive oil and garlic in a large skillet over medium-low heat. Cook the garlic until golden, stirring occasionally, 4 to 5 minutes. Remove the garlic with a slotted spoon and drain on a paper towel. Increase the heat to medium; add the stems and season with salt. Cook, stirring occasionally, until you can insert the tip of a knife into the stems without resistance, 3 to 4 minutes. Add the red pepper flakes and cook, stirring, 30 seconds.
4. Turn the heat to medium-high, add the beet greens and cook, tossing occasionally, until the greens are coated with oil and just starting to wilt. Season with salt and cook until the leaves are wilted and tender, about 3 minutes. Reduce the heat to medium-low.
5. Pour the pasta on top of the greens and salt lightly. Toss with tongs and add the reserved pasta water. Divide among 4 pasta bowls and top with reserved garlic slices and desired cheese.
Recipe courtesy of Food Network Kitchens for entwine. Copyright 2011 Television Food Network, G.P. All rights reserved