Place dark green leek trimmings, asparagus trimmings, 1 cup peas, 2 minced garlic, vegetable broth, in large saucepan. Bring to simmer over high heat, then lower heat to medium-low and gently simmer 10 minutes. While broth simmers, combine mint, chives, and lemon zest in small bowl; set aside.
Strain broth through fine-mesh strainer into 8-cup measuring cup, pressing on solids to extract as much liquid as possible (you should have 5 cups broth; add water as needed to measure 5 cups). Discard solids and return broth to saucepan. Cover and keep warm over low heat.
Heat 2 tablespoons oil in Dutch oven over medium heat until shimmering. Add sliced leeks and pinch salt; cook, covered, stirring occasionally, until leeks begin to brown, about 5 minutes. Add asparagus pieces and cook until crisp-tender, 4 to 6 minutes. Add remaining 2 minced garlic cloves and pepper flakes; cook until fragrant, about 30 seconds. Add remaining cup peas and continue to cook 1 minute. Transfer vegetables to plate and set aside. Wipe out pot.
Heat remaining 4 tablespoons oil in now-empty Dutch oven over medium heat until shimmering. Add pasta and cook, stirring frequently, until just beginning to brown, about 5 minutes. Add wine and cook, stirring constantly, until absorbed, about 2 minutes.
When wine is fully absorbed, add hot broth. Increase heat to medium-high and bring to boil. Cook, stirring frequently, until most of liquid is absorbed and pasta is al dente, 8 to 10 minutes.
Remove pot from heat, stir in lemon juice, Parmesan, half of herb mixture, and vegetables. Season with salt and pepper to taste. Serve immediately, passing Parmesan cheese and remaining herb mixture separately.