Dice the onion, peel and slice the carrots into 1/4-inch-thick rounds, and slice the celery into 1/4-inch pieces. Place these in a medium bowl. Finely chop the garlic cloves.

Cut the beef chuck into 1/2-inch cubes. Using paper towels, pat the beef dry and season with 1 teaspoon of kosher salt and the black pepper.

Heat 1 tablespoon of olive oil in a Dutch oven or large stockpot over medium-high heat until it shimmers. Place half of the beef in the pot in a single layer, browning it for approximately 2 minutes per side. Transfer the browned beef to a plate. Repeat this process with the remaining beef, adding it to the plate once browned.

In the same pot, add the remaining tablespoon of olive oil and heat until shimmering. Introduce the prepared onion, carrot, and celery mixture, cooking it while stirring occasionally, until the vegetables start to soften and become fragrant, about 3 to 5 minutes. Add the chopped garlic, dried thyme, and the remaining teaspoon of kosher salt, cooking until the garlic is fragrant, roughly 30 seconds more.

Stir in the tomato paste, coating the vegetables well, and cook until the tomato paste darkens slightly, about 1 minute. Return the browned beef and any accumulated juices to the pot. Add the beef broth, diced tomatoes with their juices, pearl barley, and the bay leaf. Stir well to combine all ingredients.

Bring the mixture to a boil over high heat, then reduce the heat to medium-low and let it simmer uncovered. Continue simmering until the barley is fully cooked and tender, which should take about 40 to 50 minutes.

While the soup simmers, chop the parsley leaves coarsely if using for garnish. Once the barley is tender, remove the bay leaf from the soup and discard it. Ladle the soup into serving bowls, garnish with the chopped parsley, and serve immediately.