Peel the beet and potato and cut both into chunks, with the potato in slightly larger chunks than the beet.
Steam both vegetables or place in a pot and cover with cold water and bring to a boil to cook until tender to a knifepoint. You can cook them together or separately, as suits - timing will depend on the size of the pieces but the potato will take around 10 minutes, beet 15 minutes. Test as you go and take out potato if ready sooner instead of cooking further.
Once cooked, drain the vegetables. Mash the potato while still warm (or use a ricer) and leave to cool. Blend the beet in a food processor until relatively smooth then allow to cool (you can speed up the beet in the fridge but I recommend potato at room temperature so it doesn't become more moist).
While the vegetables are cooking and cooling, measure out the other ingredients. Once both potato and beet are lukewarm, combine both in a large bowl and add the ricotta, parmesan and flour. Mix well, using your hands towards the end to break any chunks and distribute everything well.
Lightly flour a clean work surface and take a small handful of the dough. Roll it out into a log, roughly ½ - ⅔in (1 ½ - 2cm) diameter, flouring as you go as needed to save it sticking.
Cut slices from the log then roll each with floured hands into balls. If you like, you can give them some texture with the tips of a fork on one side or roll or a wooden gnocchi board.
Repeat with the rest of the gnocchi dough, placing on a lightly floured plate or baking sheet/tray once formed until ready to cook.
Bring a wide pot of water to a roaring boil (you want a good 2inches/5cm or more depth). Add some of the gnocchi to the water, trying to spread them out though they will drift together. Take care not to overcrowd the pot.
Once they rise to the surface, let them boil just 30 sec-1min more then remove them with a slotted spoon (or drain with a regular spoon as you go). I typically keep them in a bowl to keep warm and add further batches as they are ready. Repeat with the rest of the gnocchi then serve - I suggest with browned butter and topped with parmesan.