Squash blossom soup with mixed herb pesto

6 tablespoons butter;

1 large onion, chopped;

2 pounds summer squash, thinly sliced (about 6 cups);

2 medium carrots, thinly sliced (about 1 cup);

1 medium russet potato, peeled and chopped (about 1 cup);

4 to 5 cups chicken or vegetable stock;

11⁄2 teaspoons kosher salt, plus more to taste;

1⁄2 teaspoon ground black pepper, plus more to taste;

24 large squash blossoms (each about 3 inches long), divided;

Melt the butter in a large saucepan over medium-high heat. Add the onion and a pinch of salt and cook, stirring often, until softened but not browned at all, about 5 minutes. Add the squash and carrots and a pinch of salt. Cook, stirring often, until the vegetables are tender, about 8 minutes. Add the potato and enough stock to just cover the vegetables. Season with the salt and pepper. Bring to a boil over high heat, then reduce the heat to medium-low and simmer until the potato is tender, about 10 minutes.
Meanwhile, clean the blossoms by gently rinsing them in a bowl of cool water. Break off and discard the stems and the short green sepals at the base of the flower. Gently cut or tear open the blossoms and break loose and discard their fuzzy centers. Cut the blossoms crosswise into 1⁄4-inch strips. Stir half of the blossom strips into the soup and simmer for 3 minutes.
Puree the soup in a blender (working in batches to not fill the blender more than half full) or directly in the pot with an immersion blender. Add more stock if the soup is too thick. Season with additional salt and pepper. Just before serving, stir in the remaining blossoms and simmer only until they soften into golden ribbons. Serve hot, topped with a drizzle of Mixed Herb Pesto.
What else works? You can use thinly sliced spinach leaves in place of the squash blossoms.