Put water in a large casserole over a medium-high heat until it boils. When it boils add the pasta and cook according to the instructions on the box.
While the water boils and the pasta cooks, prepare and cook the vegetables. Chop the onions, slice the red beets, and slice the white part of the fennel bulbs into bite-sized pieces. For the fennel remove the fronds and the green parts on top. You can put the fronds aside in case you want to sprinkle them on top of the cooked dish at the end.
Pour the olive oil in a pan over a medium-high pan. When the oil is hot, add the chopped onions and sauté a couple minutes until they start softening.
Reduce the heat to medium. Add the sliced fennel. Continue to cook about 5 minutes, stirring periodically. Add the red beets and continue to cook another 5 minutes. You may need to add a little of the pasta water If the pan becomes a bit dry or the pieces start burning, The pasta water will help the vegetables to cook and for the flavors to blend together. Add the minced garlic and cook another minute. The vegetables should be cooked, yet the red beets should be slightly firm (al dente).
Remove a cup of pasta water before straining the pasta. Add a little more of the pasta water to the vegetables so you have a good consistency to add on top of the pasta. You will not need all the pasta water.
Strain the pasta. In each bowl, put about a cup of pasta. Add the vegetable mix on top. Drizzle a little olive oil, hazelnut or walnut oil on top. Not much but just to give a hint of flavor. Put the grated Parmesan cheese or crumbled goat cheese in a bowl on the table to allow each person to add it if they like. Vegans can sprinkle some nutritional yeast instead of the cheese on top of their dish.
If you prefer serving the pasta family style, mix the vegetable topping with the pasta before bringing it to the table.