Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and minced garlic to the pot. Cook for 3 to 4 minutes until the onion softens.
Stir in the rinsed split peas, sliced carrots, beef broth, diced tomatoes, and dried thyme.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 45 to 50 minutes, stirring occasionally.
Taste and season with salt and pepper. Continue simmering uncovered for 10 more minutes if you want a thicker consistency.