Step 1: Heat vegetable oil in a large cast-iron skillet or heavy-bottomed pan over medium-high heat. Add diced potatoes in a single layer and cook for 8-10 minutes without stirring to develop a golden crust.

Step 2: Flip potatoes and continue cooking for 6-8 minutes until all sides are crispy and golden brown. Season with salt, pepper, and paprika.

Step 3: Push potatoes to one side of the skillet and add diced onion to the empty space. Cook for 3-4 minutes until softened and translucent.

Step 4: Add minced garlic to the onions and cook for another 30 seconds until fragrant. Mix everything together in the skillet.

Step 5: In a bowl, whisk together eggs and milk until well combined and slightly frothy.

Step 6: Reduce heat to medium-low and add butter to the skillet. Pour in the beaten eggs and let them sit for 30 seconds.

Step 7: Using a spatula, gently scramble the eggs with the potato mixture, stirring every 30 seconds to create large, fluffy curds.

Step 8: When eggs are almost set but still slightly wet, sprinkle shredded cheese over the top and gently fold in.

Step 9: Remove from heat and let residual heat finish cooking the eggs and melt the cheese completely.

Step 10: Garnish with chopped green onions and serve immediately while hot.