Place the flour on a clean surface. Make a well in the center and add the carrot juice and olive oil. Using a fork, slowly incorporate the flour. Once the dough comes together, switch to using your hands and begin kneading the dough. Scrape any loose flour to the side. As you knead, add a bit more flour when the dough feels sticky. Continue kneading until the dough is no longer sticky and smooth; about 8 minutes. Cover with a towel and let rest for 30 minutes.
Once the dough has rested, cut off a ½” thick slice, roll between your hands and on the counter to form a rope that is about the same thickness as a pencil. Using a knife or bench scraper, cut ½” pieces then take each piece and shape on the counter or a gnocchi board. This is done by press down and forward at the same time. It might take a bit to get the pressure right, but practice will help.
Bring a salty pot of water to a boil. Add the pasta and cook until tender and floating towards the top. Strain out the pasta and save a bit of pasta water if needed for the sauce.
Heat a skillet over medium heat and add two tablespoons of butter. Let melt then add the minced garlic. Cook until fragrant, about 1-2 minutes. Remove from the heat and add the drained pasta, ricotta, lemon zest, and 3 tablespoons worth of dill. Toss until well combined and add salt/pepper to taste. Top with the pistachios and extra dill before serving.