Place bacon in a large cast iron skillet and cook over medium-high heat, turning occasionally, until crispy, 5 to 8 minutes.
Drain on paper towels; reserve most of the bacon fat in skillet.
Reduce heat to medium; cook and stir onions until starting to soften, about 5 minutes.
Add potatoes; toss to coat evenly in bacon fat.
Pour in water and cover skillet with a large lid. Cook, checking occasionally, until potatoes are tender, about 20 minutes.
Add green onions, garlic, and paprika.
Season with salt and pepper.
Make 4 wells in the potato mixture using a wooden spoon, revealing the bottom of the skillet. Pour eggs over the mixture and cook until set; about 5 minutes.
Sprinkle on some additional cheese, place the lid back on and allow to melt.