Remove the top greens and the roots of the beets. Scrub with a vegetable brush to remove any lose dirt. Cut the top greens into 2 inch widths and wash well. Set aside. Cut the beets into halves or quarters, depending on their size (about 1/2-inch, bite-sized pieces).
Place the beets on a baking sheet and toss with the olive oil, salt, and pepper. Roast for 35 to 40 minutes, turning occasionally, until the beets are well done.
In a large skillet, heat the olive oil, and add the and garlic. When golden, add the greens (and spinach) and salt and pepper to taste. Cover and cook until wilted.
Bring a large pot of salted water to a boil. Cook the pasta until al dente. Drain it, retaining 1 cup of the cooking water. Add the pasta to the beets along with the reserved cooking water and cook together for about a minute.
Serve immediately with sprinkle of Parmigiano.
I prefer to use a larger number of small beets, if you can find them. They can then be cut into halves.