Preheat oven to 400 degrees.

Line a large baking sheet with parchment paper.

Grate cheddar and Monterey Jack cheese.

Line a large plate with two layers of paper towels.

Drape bacon slices over paper towels and cover with an additional paper towel. Microwave for about 1 minute per slice (check to make sure they are not overcooked).

Remove from microwave and let cool.

Meanwhile, peel and chop onion into small pieces.

Heat a small skillet over medium-low heat, and add butter.

When butter has melted, add chopped onion.

Sauté for 8-10 minutes, stirring occasionally, until onion is softened and beginning to brown.

Pour onion into a small bowl.

Chop bacon, and add to bowl with onion.

Chill onion-bacon mixture in the freezer for 5 minutes.

Roll out puff pastry dough to an 11-inch square, then cut each side evenly into 4 pieces, so you have a total of 16 small squares.

Crack egg into a small bowl and whisk with a pinch of salt to make the egg wash.

Use a pastry brush to paint two connecting edges of a square with egg wash.

Add a small spoonful of the bacon/onion mixture and a pinch of cheese to each square and fold over one side to make a triangle.

Crimp the sides with a fork to seal.

Repeat with remaining puff pastry squares.

Lay turnovers on the baking sheet, leaving an inch or two of space between them.

Paint each with egg wash.

Bake for 18-20 minutes, until pastries are golden brown.