Trim the beets and coat in olive oil, place the beets cut side down in a deep baking dish with 1/4 inch water
Cover with foil and prick a few holes in the top, roast until a little overcooked (about 45 minutes to 1 hour)
While the beets roast, Bring a small pot of water to a boil and cook the parsley and mint briefly until vibrant, about 20 seconds then run under cool water to stop the cooking
Pat dry and roughly chop. Add the cheeses and greens to a food processor as well as some lemon zest, salt, pepper, squeeze of lemon juice and pulse to combine
When the beets are cool enough to handle, remove the skins and roughly chop. Transfer the beets to a food processor and puree until very smooth. Set aside 1/3 cup and freeze the rest
Add flour eggs and beet puree to the food processor and pulse until the liquids are evenly distributed and beads of dough form. knead for 5-10 minutes until smooth and firm
Let the dough rest for 30 minutes, then flatten out with the pasta rolling machine until setting 7. Once you have a long thin sheet of pasta, lay it on a wooden surface
Use a sturdy glass, cut as many circles as you can out of the pasta sheet, add any scraps together and wrap in plastic wrap
Spoon or pipe about a teaspoon of the filling in the center of each circle, leaving a generous rim of dough around it, add a bit of water to the edges of the circles
Fold each circle into a half-moon, meeting opposite curves first then gently press out any air around the filling on each side. Once encased, press the edges firmly to seal
Position the half moon so the curved edge is facing downward. Then make a generous indentation in the center of the filling pocket with your finger (it will look like a smile)
Bring the two points of the half-moon around in a circular motion toward the top, overlap them slightly, and pinch firmly to seal. you should have a little gap in the center and the cappelletti should stand up on their own
Bring a large pot of water to a boil, peel 2 long strips of zest from a lemon and then thinly slice lengthwise into thin strands
Add the pine nuts to a dry skillet and toast for 3 minutes
Add the lemon zest and stir, then add butter until melted (salt if using unsalted butter)
Cook the cappelletti until tender, about 2 to 3 minutes. Transfer the cappelletti to the butter sauce and toss gently to coat. Keep the pan moving