Preheat the oven to 350F. Bake the beetroot wrapped in foil with a pinch of salt and the olive oil for 45-50 minutes until tender. Once cooled, peel and puree to a smooth consistency. This can be done 1-3 days ahead and refrigerated. Bring to room temperature before using.
Take the semolina on a clean work surface. Make a well in the middle and add the egg yolk and beet puree to it. Mix until you get a ball of dough. If the dough is dry, add some egg whites/water. If the dough is wet, add more flour. Cover and let it rest for 30-40 minutes.
Pass the dough through a pasta maker and shape according to taste and cook the pasta until al dente.
To the cooked pasta, add coarsely chopped toasted walnuts, feta cheese, finely chopped dill leaves and marinated fava beans (https://www.feastingathome.com/marinated-fava-beans/).