2/3 cup freshly grated Parmigiano-Reggiano or Pecorino Romano
Heat the olive oil and 1 tablespoon of butter in a large saute pan over medium heat. Add the onions and cook until they begin to brown and are soft.
Meanwhile, bring a large pot of salted to a boil for the pasta. Bring a large sauce pan of water to a boil, add the asparagus, and cook for 1 minute. Add the sweet peas and cook for 30 seconds, then drain. Add the asparagus and peas to the onions, then stir in the cream. Set the pan aside while you cook the pasta.
Add the pasta to the boiling water and cook until al dente. Drain and transfer to the pan with the onions.
Place the pan over high heat and cook, tossing, for 1 to 2 minutes, until the vegetables are hot. Add the herbs, arugula, 1/2 cup of the cheese, the vanilla, lemon zest, and the remaining 1 tablespoon of butter and vanilla and toss well to combine. Season with salt and pepper and a good squeeze of lemon juice.
Serve in warm bowls, garnished with more herbs and the remaining grated cheese.