Set two salted pots of water to boil, one small; one large.

Boil the English peas for 3 minutes, then drain and set aside. Add the pasta to the larger pot of boiling water (you will cook it just short of al dente).

While the pasta is cooking, heat the butter in a large skillet over medium heat. Add the garlic and asparagus, and saute for 2 minutes. Add the wine, and cook for a further 2 minutes. Reduce the heat to medium-low.

Add the cream and lemon zest, and heat to a gentle simmer, then add the cheese and stir until well-combined. Stir in the peas. Season with salt and pepper, and set aside.

Drain the pasta, add to the skillet, and stir to coat. Add the pea shoots, and cook for a minute or two over medium-low heat, until the pea shoots have just begun to wilt. Remove from heat. Squeeze lemon generously over the finished dish, and stir to combine.

Divide the pasta evenly between four serving dishes, top with mint and Parmigiano-Reggiano, and serve.