Heat 1 tablespoon olive oil in a large pot over medium heat. Add the finely chopped onion, minced garlic, and sliced celery. Sauté, stirring occasionally, until the onion is translucent and soft and the garlic is fragrant (about 5–7 minutes). Avoid browning the garlic.
Stir in the diced carrots. Pour in 4 cups vegetable or chicken broth, add a pinch of salt and pepper, dried thyme, and 1 bay leaf. Bring to a gentle boil, then reduce to a low simmer, cover, and cook for 25–30 minutes until the vegetables are tender. Skim any foam from the surface as needed.
Stir in 1 cup cooked barley or rice and simmer uncovered for 5–10 minutes to warm through. Taste and adjust seasoning with salt, pepper, and a splash of lemon juice if desired. Serve hot with fresh herbs and a drizzle of olive oil.