1. Preheat oven to 400°. Set a rack in a rimmed baking sheet and lay prosciutto slices on rack.
2. Arrange asparagus in a single layer on another baking sheet. Drizzle with 1 tsp. oil. Sprinkle with salt and pepper; toss to coat.
3. Bake prosciutto and asparagus until prosciutto is crisp and very light brown around the edges, about 8 minutes, and asparagus is a little darker and tender when pricked with the tip of a knife, 12 to 15 minutes. Remove both from oven and let cool. When cool enough to handle, cut asparagus into 1-in. pieces. Break prosciutto into small shards.
4. Pour broth into a medium saucepan and bring to a simmer over medium heat.
5. Heat remaining oil in a large pot over medium-high heat. Add onion and cook, stirring occasionally, until limp but not brown, about 5 minutes. Add rice and cook, stirring constantly, until edges turn bright white, 5 minutes. Add wine; bring to a boil and cook until almost evaporated, about 2 minutes.
6. Add one ladleful, about 1/2 cup, of broth to rice and cook, stirring, until almost completely absorbed by rice. Continue adding broth 1/2 cup at a time, stirring until each addition is absorbed before adding the next, until rice is just tender to the bite, 15 to 30 minutes (you will have broth left over).
7. Stir in mint, ricotta, peas (if using fresh), and lemon juice and stir until most of lemon juice is absorbed. Add butter and shredded cheese; stir until well mixed. Stir in peas (if frozen), asparagus, and pepper to taste.
8. Divide risotto among bowls or plates. Top with prosciutto crisps and sprinkle with shaved cheese. Serve immediately.