Step 1: Heat olive oil in a large (10-12 inch) oven-safe skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until completely browned. Drain any excess grease.
Step 2: Add the chopped onion to the skillet with the ground beef and cook for 3-5 minutes, or until softened and translucent. Stir in the minced garlic and cook for another minute until fragrant.
Step 3: Add the diced potatoes to the skillet. Season with salt, black pepper, smoked paprika, and dried thyme. Stir everything together until the potatoes are well coated.
Step 4: Pour in the beef broth and bring to a simmer. Reduce the heat to low, cover the skillet, and cook for 15-20 minutes, or until the potatoes are tender when pierced with a fork.
Step 5: Remove the lid. If there's still a lot of liquid, increase the heat slightly and cook uncovered for a few minutes to allow some evaporation.
Step 6: Sprinkle the shredded cheddar cheese evenly over the top of the potato and beef mixture. If using an oven-safe skillet, place it under a preheated broiler for 2-3 minutes, watching carefully, until the cheese is bubbly and lightly browned. Alternatively, cover the skillet again for 2-3 minutes until the cheese is fully melted.
Step 7: Remove from heat. Garnish with fresh chopped parsley and optional green onions. Serve hot directly from the skillet.