Boil whole potatoes in water over medium-high heat for 15 to 20 minutes, until potatoes are fork tender all the way through. Drain in a colander and let sit until cool enough to handle. Peel and cut into 1/2-inch dice.

In a large oven proof skillet, preferably cast-iron, heat the olive oil over medium-high heat. Add the onions and cook, stirring often, until softened, about 3 minutes. Add the potatoes, reduce the heat to medium, and cook, turning occasionally with spatula, until the onions and potatoes are lightly browned, 5 to 7 minutes, adding more olive oil as necessary. Season generously with salt and pepper.

Add the turkey to the skillet and cook, turning with the spatula, until heated through and crispy around the edges, about 5 minutes. Add the barbecue sauce and cook, turning until mixed well and heated through.

Preheat oven to 400˚F. Make 4 equidistant indentations on the top of the hash with a large spoon, crack an egg into each indentation and bake for 5 to 7 minutes or until eggs are set and the hash is lightly browned on top.

Serve immediately.

Note: You can serve hash without the egg.