In a medium nonstick skillet, heat the oil, two turns of the pan, over medium high. Add the turkey; season with coriander, cumin, granulated garlic, oregano, salt and pepper. Cook, breaking up with a spoon, until browned and cooked through, about 5 minutes. Add the stock, ketchup, vinegar, sugar, hot sauce and Worcestershire. Simmer the BBQ turkey, stirring often, until the sauce thickens, about 12 minutes.
Meanwhile, in a large nonstick skillet, melt 2 tbsp. butter over medium-high. Add the onion, potato, apple and thyme; season. Cook, stirring often, until browned, about 15 minutes. Wipe skillet clean to cook the eggs, if using.
Heat a griddle pan over medium-high.
If adding eggs to the filling, melt 1 tbsp. butter in reserved skillet over medium. Crack the eggs into the skillet; fry until cooked to over-easy or over-medium, 3 to 4 minutes.
Assemble the burritos by placing a quarter of the BBQ turkey and the hash, 1 egg, if using, and a quarter of the cheese along the lower third of each tortilla. Fold in the sides, then roll up tightly.
Lightly spray the burritos with cooking spray. Add to the griddle pan, seam side down; cook until crispy and browned, about 2 minutes per side. Cut in half.