In a skillet over medium heat, add 2 teaspoons of oil and heat until shimmering. Add spring onions and cook until soft and slightly browned. Add garlic and fresh herbs and cook until fragrant. Slowly whisk in chicken broth and bring to a simmer. Remove from heat, add peas, cover, and set aside.
Bring a large pot of salted water to a boil. Add asparagus and cook until bright green and just tender. Use a skimmer to remove asparagus from water and set aside. Add conchiglie to water and cook according to package directions. Drain and toss with spring onion mixture and asparagus.
In a large skillet, heat remaining 2 teaspoons of olive oil over high heat until shimmering. Add pork and cook, breaking up, until pork is cooked through and browned all over. Remove pork from skillet, reduce heat to medium, and add butter. Once butter has stopped bubbling, add bread crumbs and cook until crisp and toasted, about 3 minutes.
Add cooked pork and bread crumbs to pasta and toss. Add about half of the cheese and toss again. Serve topped with the rest of the cheese.