Spring Vegetable Egg Drop Soup

1/4 cup olive oil

3 medium carrots, peeled, chopped

1 large onion, chopped

3 garlic cloves, minced

Kosher salt

6 cups low-sodium chicken broth

1/2 pound asparagus, sliced on a diagonal 1/2" thick

1/4 pound sugar snap peas, sliced on a diagonal 1/4" thick

1 cup frozen peas

4 large eggs

2 tablespoons grated Parmesan plus more for serving

1/4 cup torn fresh basil leaves

1/4 cup torn fresh mint leaves plus extra whole leaves for garnish

1 1/2 teaspoons (or more) fresh lemon juice

Heat oil in a large heavy pot over medium heat.  Add carrots and onion and season with salt.  Reduce heat to medium-low, cover and cook, stirring occasionally, until vegetables are soft, 15-20 minutes.  Add garlic and cook for 1-minute.  Add broth and bring to a boil.  Add asparagus, sugar snap peas, and frozen peas and cook until vegetables are tender, about 3 minutes.  Meanwhile, beat eggs in a small bowl with 2 tablespoons Parmesan, a pinch of salt, and 1 tablespoon water.  Reduce heat to low and stir basil and mint into soup.  Drizzle in egg mixture in 4 or 5 spots around pot.  Let stand for 1 minute so egg can set, then gently stir in 1 1/2 teaspoons lemon juice.  Season soup with salt and more lemon juice, if desired,  Serve soup topped with more Parmesan and garnish with mint leaves.