In a large bowl, whisk together the flour and salt.
Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Gradually add the ice water, 1 tablespoon at a time, mixing until the dough just comes together. Do not overmix.
Gather the dough into a ball, flatten it into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Assemble the Galettes
Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
On a lightly floured surface, divide the dough into 4 equal portions. Roll each portion into a circle about 8 inches in diameter.
Transfer each dough circle to the prepared baking sheet.
Sprinkle the crumbled bacon and shredded cheese over the center of each dough circle, leaving a 2-inch border.
Carefully create a small well in the center of the filling for each egg. Crack one egg into each well.
Fold the edges of the dough up and over the filling, pleating as you go, to create a rustic crust.
In a small bowl, whisk together the egg and milk for the egg wash. Brush the crust with the egg wash.
Bake and Serve
Bake for 20-25 minutes, or until the crust is golden brown and the egg whites are set but the yolks are still runny. If the crust is browning too quickly, loosely tent with foil.
Sprinkle with fresh chives before serving.
Notes
For a spicier kick, add a pinch of red pepper flakes to the cheese mixture.