Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente.
While the pasta is working, in a large saucepan, heat 2 tablespoons EVOO, 2 turns of the pan, over medium-high heat. Add the onion and cook until softened, 5 minutes. Stir in 1 1/2 cups chicken broth, the peas and lemon peel; simmer for 2 minutes. Using a food processor, puree half of the pea mixture. Add to the pea mixture in the skillet and stir in one-third of the pasta, the basil and 1/3 cup Parmesan; season with salt and pepper. Transfer to a bowl; keep warm. Wipe out the saucepan and food processor.
In another saucepan, combine the carrots, 1 1/2 cups chicken broth, the butter and honey; season with salt and pepper. Simmer until the carrots are tender when pierced with a fork, about 10 minutes. Using the food processor, puree the carrots. Return the carrot puree to the saucepan and stir in one-third of the pasta, the chives and 1/3 cup parmesan; season with salt and pepper. Transfer to a serving bowl and keep warm. Wipe out the food processor.
In the reserved saucepan, heat the remaining 2 tablespoons EVOO , 2 turns of the pan, over medium heat. Add the garlic and cook until golden, 2-3 minutes. Using the food processor, puree the roasted peppers. Add the puree to the garlic in the skillet and stir in the remaining 1 cup chicken broth. Stir in the remaining pasta and Parmesan and the parsley; season with salt and pepper.
Serve a quarter of each pasta to each person.