How to Make It
Make the Carrot Juice Cavatelli: In a food processor, blend together the flour and salt. With the machine running, slowly add the carrot juice (you may not need all of it), until the dough comes together. Be careful not to overwork the dough in the food processor: The dough may well look crumbly, but if you press it together with your fingers it should very easily combine into dough. You are looking for a texture similar to Play-Doh: elastic, pliable, and not sticking to your fingers when you touch it. If the dough is too dry, add more juice; too wet, add more flour.
Transfer the dough to a lightly floured surface and knead it with the heels of your hands for about 1 minute, until you have a smooth dough. Wrap the dough tightly with plastic wrap (clingfilm) and let it rest overnight in the refrigerator. Place the carrot pulp on a dehydrator tray and dehydrate at 135ºF (57ºC) overnight.
About 1 hour before you plan to make the cavatelli, let the dough come to room temperature–– this will make it much easier to work with. Divide the dough into 6 pieces. Lightly flour a work surface. Working with one piece at a time–– and keeping the rest of the dough covered–– roll the dough into a long, thin rope, about 1/8 inch (3 mm) in diameter. Cut the rope crosswise into 1/4-inch (6 mm) pieces.
Using a cavatelli board, or the tines of a fork, gently but confidently roll the dough pieces against it. The cavatelli may not come out perfect right away, but soon the motion will find its way into your muscle memory.
Once the cavatelli are shaped, lay them in a single layer (not touching) on a baking sheet lined with a tea towel. Repeat this process until all of the dough has been turned into cavatelli. These are best cooked when fresh, so if you are going to be cooking them the same day, you can just leave them out. Otherwise, cover and refrigerate for up to 2 days.
Bring a large pot of water to a boil. Season your water with salt so it tastes like the sea. I think it’s important to taste the pasta water to make sure it is seasoned properly. Once seasoned and boiling, add the cavatelli and cook until they float to the surface, about 3 minutes. If you’re not sure whether they are done, the best test is just to eat one.
To Serve: While the pasta water heats up, gently warm the carrot purée in a small pan over low heat and keep covered (and warm) until serving.
Using a sieve, scoop the cavatelli out of the pasta water and into a wide bowl. Immediately dress them with the carrot top salsa verde and toss to combine. Ladle in some of the starchy, seasoned pasta water, a little at a time, to open up the flavors and create a very light sauce that will coat the cavatelli. Don’t add too much water or it will make for a thin, diluted sauce.
Place dollops of the carrot purée on 4 warmed plates. Spoon the cavatelli on top and sprinkle the carrot crumble over the pasta and the plate. I like being able to drag the cavatelli through more of the crumble as I’m eating it. Shave ribbons of Gouda over the top and serve immediately.