Ask a GH (Grown-Up Helper) to bring a large pot of water to a boil. Salt it, add the pasta and cook until al dente. Have your GH set aside a ladle of pasta cooking water and drain the pasta.
While the pasta is cooking, put the peas and broth in a small saucepan. Have your GH simmer the peas in the broth for 5 minutes.
In a large serving bowl, mash half the peas and broth with the ricotta cheese. Toss with the pasta, butter and half the Parmigiano-Reggiano cheese. Add the reserved pasta cooking water to moisten if needed. Stir in the remaining whole peas and the basil; season with salt and pepper. Top with the remaining Parmigiano-Reggiano cheese.