Spring Egg Drop Soup

Name: Spring Egg Drop Soup
Ingredients: 1 /4 cup olive oil; 2 medium carrots, peeled, choppedt; 6 small spring onions, bulbs only, coarsely chopped (about 1 1/2 cups); 3 medium spring garlic bulbs, 1-2 garlic scapes, or 2 regular garlic cloves, thinly sliced; Kosher salt; 4 cups low-sodium chicken broth; 1 /2 pound asparagus, sliced on a diagonal 1/2-inch thick; 1 /4 pound sugar snap peas, sliced on a diagonal 1/4-inch thick; 2 /3 cup shelled fresh peas (from about 2/3 pound pods); 2 large eggs; 1 tablespoon grated Parmesan plus more for serving; 1 /4 cup torn fresh basil leaves; 1 /4 cup torn fresh mint leaves; 1 1/2 teaspoons (or more) fresh lemon juice