Heat the olive oil in a large skillet over medium heat.
Add the diced potatoes, salt, pepper, and paprika. Cook for about 10 minutes, stirring occasionally, until the potatoes are golden and beginning to crisp on the outside.
Add the diced onion and bell pepper to the skillet. Continue cooking for 4 to 5 minutes, stirring occasionally, until the vegetables are softened. Stir in the minced garlic and cook for about 30 seconds until fragrant.
Using a spoon, make four small wells in the potato mixture. Crack one egg into each well.
Cover the skillet and cook for 4 to 5 minutes, or until the egg whites are set and the yolks reach your desired doneness.
Sprinkle the shredded cheddar cheese over the skillet, if using, and let it melt for 1 to 2 minutes. Remove from heat and serve immediately.