Step 1

On the large holes of a box grater, shred the potato. Transfer to a fine-mesh sieve and rinse with cold water until the water runs clear. Drain well, then wrap in a clean kitchen towel or cheesecloth and squeeze out any remaining moisture. Transfer to a medium bowl and season with salt and black pepper to taste.

Step 2

In a large skillet set over medium-high heat, cook the bacon, if using, tossing occasionally, until golden brown, 8–10 minutes. Transfer to a paper towel-lined plate and set aside to cool slightly. In the same skillet, melt 1½ teaspoons of the butter. Add the potato and, using a spatula, press into a flat, even layer (about ½ inch thick). Cook until the bottom is crispy and golden brown, 5–7 minutes, then flip in sections to cook the other side, 5–7 minutes more. Transfer to a separate paper towel-lined plate and set aside.

Step 3

In the same skillet, melt the remaining butter. Crack in the eggs, season with salt and black pepper to taste and, using a spatula, scramble until the eggs are just set, 3–4 minutes. Transfer to a plate and set aside.

Step 4

In a medium bowl, gently toss together the bacon (if using), potato, and chiles, and set aside.

Step 5

In a large, heavy-bottomed skillet or griddle set over medium heat, warm one of the tortillas, flipping once, until pliable, about 1 minute. Remove from the heat and repeat with the remaining tortilla.

Step 6

Assemble the burritos: On a clean work surface, top each tortilla evenly with the cheese (leaving a 1-inch border around the edge), followed by the eggs, and then the potato mixture. Working with one tortilla at a time, fold two sides of the tortilla inward, then roll up the two opposite sides tightly. Repeat with the remaining tortilla. In the same skillet set over medium-low heat, place the burritos seam side down and cook until sealed and golden brown, 2–3 minutes. Turn to cook the other side, 2–3 minutes more. Serve with red or green chile sauce, or both, on the side or spooned on top.