Melt 2 tablespoons of unsalted butter over medium heat in a large stockpot until it foams. Add chicken legs and brown for 5-7 minutes on each side. Remove chicken and set aside.

In the same pot, add diced yellow onion, sliced carrots, and chopped celery. Sauté for around 5 minutes until softened. Stir in 3 minced garlic cloves and cook for 1 additional minute.

Return the browned chicken to the pot and pour in 6 cups of chicken broth. Season with 1 teaspoon kosher salt, 1/2 teaspoon black pepper, and add dried thyme, rosemary, oregano, and 2 bay leaves. Bring to a simmer.

Stir in 2 cups of chopped red potatoes and 1 cup of barley. Reduce heat to medium-low and cover, simmering gently for 25-30 minutes.

After barley and potatoes are tender, add 1 can of diced tomatoes, 1 cup of green beans, and 1 chopped zucchini. Stir and continue to simmer uncovered for 10-15 minutes.

Stir in 1 cup of frozen green peas and cover. Cook for about 5 minutes until peas are heated through. Adjust seasoning if necessary before serving.

Ladle the soup into bowls, ensuring each contains tender chicken and vegetables. Serve with crusty bread for dipping.