Preheat the oven to 400 F/ 200 C/ gas mark 6. Peel the beetroot, cut in half and slice thinly, then toss into a large baking tray. The slices can overlap each other. Crumble the feta over the beetroot. Combine the garlic with 4 tablespoons of the oil and drizzle over the whole thing. Bake for 30 minutes.
In the meantime boil the pasta, drain and combine with the arugula and the remaining oil. Season to taste. Combine with the beetroot, drizzle with a little more oil if you like and enjoy!
Serve hot or cold, as a main, salad or side dish.
Slice the beets quite thinly, to about 5mm of thickness (they will roast faster!) This really doesn't take very long and the slices don't have to be identical (my advice is to wear rubber gloves though as the beetroot will stain your hands).
I recommend orzo pasta or another small pasta variety, such as soup pasta.
Serve this pasta salad warm or chilled. If you prefer it warm cook the pasta while the beetroot is in the oven so you can combine these mixtures as soon as the beetroot is ready. If you are planning to serve it cold you can cook the pasta, as well as the beetroot (and feta) ahead and refrigerate these (for up to 2 days) until you are ready to make the recipe.