To make the pico de gallo, combine all the ingredients into a medium bowl. Mix until combined. Taste and add salt to personal preference. Set aside or cover and refrigerate until ready to build the burritos.
To make the chipotle sauce, add all the ingredients together in a food processor or blender. Blend until smooth. Taste and adjust salt to personal preference. Set aside or in the refrigerator until ready to serve the breakfast burrito.
For the breakfast burrito, add the eggs with the milk in a medium bowl and whisk. Add 1/2 tablespoon of the butter or oil into a medium skillet over medium heat. Pour in the eggs.
Stirring frequently, scramble the eggs until the eggs are set. Add salt and pepper to taste.
Lay out a large tortilla. Add the scrambled eggs to the middle. Top cooked fries, pico de gallo, and cheddar cheese.
Fold in the sides of the tortilla and then carefully roll the tortilla into a burrito.
Add the remaining 1/2 Tablespoon of butter or oil into a clean skillet over medium heat. Once hot, add the burrito, seam side down. Once golden brown, flip and brown the other side.
Remove the skillet and enjoy immediately with the chipotle sauce for dipping.