Cut the potatoes lengthwise into ¼-inch x ¼-inch thick slices. Put the fries into a large bowl of cold water and refrigerate for at least 1 hour.
Heat a deep-fryer or a large heavy-bottomed pot filled with enough oil to reach at least 3-inches up the pot over medium heat to 350ºF (180ºC). In a medium mixing bowl whisk together the flour, salt, garlic powder, paprika, pepper and cayenne. Slowly add enough cold water to form a thin batter, about 1½ cups. Dip the fries in the batter and add to the oil. Fry until golden brown and crispy, about 5 minutes. Remove to a paper towel lined plate to drain.
For the grilled chicken:
Rub the chicken with the olive oil then season with salt and pepper on both sides. Heat grill to medium-high heat. Add the chicken to the grill and cook until browned and char marks start to appear, about 5 minutes. Flip and continue to cook until the chicken is browned and just cooked through (or reaches an internal temperature of 165ºF/ 73.8ºC), about an additional 4 minutes.
Remove to a cutting board and let cool. Chop the chicken into 1-inch cubes and set aside.
For burrito assembly:
Heat a large nonstick skillet over medium heat. Working one at a time add a tortilla to the pan and sprinkle 1 cup of the cheese over the top, cooking until the cheese just melts. Remove to a clean workspace and add the lettuce, half of the chicken, slices of avocado, ¼ cup of the pico de gallo and a handful of fries.
To assemble the burrito, fold the bottom half over the top half then pull the tortilla back to form the filling into a roll. Fold one side in then the other, then tightly roll the burrito.
Add the burrito, cut side down to the skillet and cook until golden brown, about 2 minutes. Flip and brown the other side, about another 2 minutes. Remove and cut in half then serve immediately. Repeat with the remaining tortilla and ingredients.
Notes
Let the fries cool slightly before adding them to the burrito so they stay crispy longer and don’t steam inside the tortilla.