Heat the oil in a large nonstick skillet over medium-high heat.
Add the diced potatoes and spread them into a single layer. Let them cook without stirring for about 2 minutes, or until lightly golden underneath.
Stir the potatoes, spread them out again, and cook for another 2 minutes to develop more golden-brown edges.
Push the potatoes to one side of the skillet. Add the ground beef to the empty side and season both the beef and potatoes evenly with salt and black pepper.
Break the ground beef into smaller pieces with a wooden spoon and spread it across its half of the skillet. Cook for about 4 minutes, stirring the potatoes occasionally.
Carefully spoon out any excess fat from the skillet if necessary.
Add the chopped onion, bell pepper, minced garlic, and smoked paprika. Stir everything together until evenly combined.
Continue cooking for 3–4 minutes, stirring occasionally, until the beef is completely cooked, the vegetables are tender, and the potatoes are easily pierced with a fork. The beef should reach a safe internal temperature of 160°F (71°C).
Turn off the heat and sprinkle the cheddar evenly over the Ground Beef and Potato Skillet. Let the residual heat melt the cheese.
Finish with chopped green onions and serve warm.