Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Sauté for 5-7 minutes until vegetables begin to soften.
Add minced garlic and cook for another minute until fragrant.
Pour in the vegetable broth and add the pearl barley. Stir in smoked paprika and thyme.
Bring to a boil, then reduce heat to low and simmer for 30-35 minutes until barley is tender.
Add frozen peas and cook for another 5 minutes until heated through.
Using a potato masher or the back of a spoon, gently smash about half of the peas and barley to create a chunky, thick texture.
Season with salt and pepper to taste. Serve hot, garnished with fresh parsley.