In a 6-quart soup pot, heat 2 teaspoons of the olive oil over medium-high heat. Add the meat and brown evenly, about 5 minutes. Using a slotted spoon, transfer the meat to a paper towel-lined plate.
Reduce the heat to medium. Add the remaining oil and the onion and cook until the onion is soft and translucent, about 10 minutes, scraping the pot to loosen any brown bits.
Add the carrots and garlic and sweat 5 minutes, stirring occasionally. Add 1/2 cup of stock and scrape the bottom of the pot. Add the remaining stock, the meat, barley, and thyme and bring to a boil.
Reduce the heat and simmer, skimming the pot occasionally, until the barley is cooked and the meat is tender, about 50 minutes.
Ladle into deep bowls and serve, garnished with parsley.