Pat the beef cubes dry and season with salt and pepper. Heat the olive oil in a Dutch oven over medium-high; brown the beef in a single layer, about 4 minutes per side, then transfer to a plate.
Reduce the heat to medium, add the onion, carrots, and celery, and cook 5 minutes, scraping up the browned bits, until softened.
Stir in the garlic and tomato paste and cook 1 minute, until fragrant.
Add the broth, barley, thyme, and browned beef. Bring to a boil, then reduce to a gentle simmer.
Cover and simmer 50 minutes, stirring occasionally, until the beef is fork-tender and the barley is plump.
Stir in the frozen peas and simmer 5 minutes more. Taste and adjust the salt and pepper, then serve hot; thin with a splash of broth if the soup thickens too much.