Warm the oil in a generous-sized non-stick skillet over medium-high heat.
Place the diced potatoes in the skillet in a single layer and let them brown undisturbed for about 2 minutes. Then stir and let them brown again for another 2 minutes without stirring.
Push the potatoes to one side of the skillet with a wooden spoon and add the ground beef on the other side. Season both the potatoes and beef with salt and pepper evenly.
Break apart the ground beef with the spoon and spread it out to cover its side of the skillet. Press the beef down and let it cook for 4 minutes without moving it, while giving the potatoes a gentle stir now and then.
Remove any extra fat from the beef if you want by carefully spooning it out.
Add the onion, bell pepper, minced garlic, and smoked paprika on top of the potatoes and beef. Stir everything together to mix evenly.
Keep cooking, stirring now and then, until the veggies are soft, the beef is fully cooked, and the potatoes are tender when poked, about 3 to 4 minutes.
Turn off the heat and sprinkle the shredded cheddar cheese over the skillet. Let the cheese melt from the residual heat.
Finish by scattering the chopped green onions on top and then serve immediately.