Heat a large pot of water to a boil, salt liberally and cook pasta to al dente.
While pasta cooks, you will need 3small skillets set up and a food processor near by. Set up 3 serving dishes that would hold half a pound of pasta each on a counter near the stove.
In first skillet, melt butter with olive oil over medium heat, add onion, season with salt and pepper, to taste, and sweat 5 to 6 minutes. Add stock and zest and bring to a boil. Add peas, season with salt and pepper and heat through, about 2 minutes. Put in food processor and process until a smooth sauce forms and transfer to a bowl, fold in fresh ricotta, basil and mint with rubber spatula, adjust seasoning salt. When pasta is ready, add a ladle of pasta water or chicken stock, if needed and 1/3 of the pasta to the bowl. Toss the pasta with sauce.
In the second skillet while peas are cooking, add chicken stock, carrots, curry powder, hot sauce, salt and pepper, to taste, honey and butter. Bring to a boil and let simmer to heat through, 10 minutes.
While carrots are cooking, grind roasted peppers into a paste. Heat 2 tablespoons olive oil in third pan over medium-low heat and saute the garlic and red pepper, stir in ground peppers and season with salt and freshly ground black pepper. Rinse processor bowl and return to base to grind the carrots when they are tender. When peppers are hot, stir in balsamic vinegar and parsley and let simmer over low heat. Stir in starchy cooking liquid or stock, scrape sauce into serving dish and coat 1/3 of the pasta and cheese.
Grind carrots into a smooth paste and transfer to a serving dish. Thin carrot sauce with starchy liquid or stock and toss with remaining half pound of pasta and chives.
Each of the 3 sauces will require a ladle of starchy cooking liquid taken just before draining pasta or chicken stock, optional.