Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.

Add canola oil to a 12-inch nonstick pan over medium heat. Add potatoes, salt, and pepper. Fry until potatoes are fork-tender, about 20 minutes. Transfer to a medium bowl.

Add sausage and onion to the same pan. Cook and stir until onion is translucent, about 5 minutes. Transfer to the bowl of potatoes using a slotted spoon. Stir in green chiles. Allow mixture to cool to room temperature.

Divide each pie crust into 3 pieces. Roll out each piece into an 8-inch circle. Add 3 tablespoons of the potato-sausage mixture to each circle. Mix Cheddar and Gouda cheeses together; sprinkle 3 tablespoons over the filling.

Beat egg and milk together to make egg wash. Fold dough over the filling in a semi-circle shape. Brush the edge of the pastry with egg wash; press to seal. Flute the border with a fork. Brush the tops with egg wash and score tops with a fork.

Space hand pies evenly on the prepared baking sheet.

Bake in the preheated oven until golden brown, about 20 minutes.