Prepare the Hash Browns: Begin by peeling the russet potatoes and grating them using a box grater or food processor. Transfer the grated potatoes to a clean kitchen towel and squeeze out excess moisture; set aside while you preheat your skillet to medium heat.

Cook the Hash Browns: In a large non-stick skillet, melt 1 tablespoon of butter over medium heat. Once melted, add the grated potatoes evenly to the skillet, spreading them out to form a flat layer. Cook for about 5-7 minutes without stirring, until the underside is golden brown and crispy. Flip and cook for an additional 5-7 minutes.

Scramble the Eggs: Crack the eggs into a mixing bowl and whisk them with a pinch of salt and pepper. When the hash browns are crispy on both sides, create a space in the center of the skillet and pour the egg mixture over the top. Gently scramble the eggs with a spatula until softly set and slightly creamy.

Add Cheese and Vegetables: Once the eggs are nearly cooked, sprinkle the shredded cheddar cheese, diced bell peppers, and onions over the hash browns and scrambled eggs.

Melt the Cheese: Cover the skillet with a lid and let it cook for an additional 1-2 minutes, or until the cheese is gooey and bubbly.

Serve and Garnish: Remove the skillet from heat, uncover, and top your dish with optional salsa, avocado, or sour cream. Serve hot.