Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a ladleful of the pasta cooking water.
While the pasta is working, bring a large saucepan of water to a boil, salt it, add 1 box of peas and cook for 2 minutes; drain. Transfer to a food processor and puree with the mint, parsley and ricotta; season with salt and pepper. Transfer to a large serving bowl.
In a medium skillet, heat the EVOO, 2 turns of the pan, over medium heat. Add the shallots and cook for 3 minutes. Add the wine, lower the heat and bring to a simmer, then add the remaining box of peas and heat through; season with salt and pepper.
Stir the reserved pasta cooking water into the ricotta mixture. Add the pasta and the shallot-pea mixture and toss; season with salt and pepper. Top with the radishes and pea sprouts.