Melt 2 tablespoons of unsalted butter in a large stockpot over medium heat. Add the chicken legs to the pot and brown them on all sides, about 8-10 minutes total. Once browned, remove the chicken and set it aside.

In the same pot, add the diced yellow onion, carrots, and celery, sautéing for about 5 minutes until softened. Stir in minced garlic, cooking for an additional minute until fragrant.

Return the browned chicken to the pot, pour in 6 cups of chicken broth, and add 1 teaspoon each of kosher salt and black pepper, along with the dried herbs and bay leaves. Bring to a simmer and let it meld for about 5 minutes.

Stir in the chopped red potatoes and 1 cup of barley. Let it simmer gently for 25-30 minutes until the potatoes and barley are tender.

Mix in the canned diced tomatoes, green beans, and zucchini. Simmer for an additional 10-15 minutes until all vegetables are cooked through.

Add 1 cup of frozen green peas, stirring them into the soup. Cook just until they are heated through, about 2-3 minutes.

Ladle the hot soup into bowls, ensuring each serving has chicken, vegetables, and grains. Serve immediately, ideally with crusty bread.