Shredded cheddar and sour cream for topping, optional.
In a large non-stick skillet, add the ground beef and season generously with salt and pepper. Cook on medium heat, breaking the beef into small crumbles as it cooks. When it is mostly done with just a bit of pink remaining (don't worry, it'll finish cooking later) remove the beef to a bowl or plate and set aside, reserving the grease in the skillet.
Add the onions and radishes to the skillet and cook for 5-7 minutes, stirring frequently.
Add the tomato paste, broth, Worcestershire sauce, oregano, thyme, and the carrots. Mix well. Reduce heat to low, cover, and allow to cook for about 20 minutes or until the radishes start to get tender.
Add the ground beef back to the pan, mix, and allow to cook, covered, for an additional 10-15 minutes or until radishes are fully tender and beef is finished cooking.
Taste and adjust seasonings as needed. If the mixture looks a little dry, add extra beef broth.
Serve as-is or with shredded cheddar cheese and sour cream.