Heat a large pot over medium heat and add the beef stew meat. Brown the meat on all sides for about 5 minutes, stirring occasionally.
Add the diced onion, sliced carrots, sliced celery, and minced garlic to the pot. Cook for 4 minutes until the vegetables begin to soften.
Stir in the pearl barley, beef broth, diced tomatoes, dried thyme, salt, and black pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 45 minutes until the barley is tender and the beef is cooked through.
While the soup simmers, preheat the oven to 400 degrees and line a muffin tin with paper liners.
In a mixing bowl, whisk together the cornmeal, all-purpose flour, baking powder, sugar, and salt. In a separate bowl, mix the milk, egg, and melted butter.
Pour the wet ingredients into the dry ingredients and stir just until combined. Spoon the batter evenly into the prepared muffin tin.
Bake the muffins for 15 minutes until the tops are golden and a toothpick inserted in the center comes out clean. Serve the muffins warm alongside the soup.