In a mixing bowl, combine the flour and salt. Add the cold butter and mix until the mixture resembles coarse crumbs.
Gradually add ice water, one tablespoon at a time, mixing until the dough comes together. Form the dough into a ball, wrap in plastic wrap, and refrigerate for 30 minutes.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the dough into a circle about 1/8 inch thick. Transfer to the prepared baking sheet.
Sprinkle the cheese evenly over the dough, leaving a 1-inch border around the edges.
Arrange the chopped bacon over the cheese. Carefully crack the eggs on top of the bacon, ensuring they stay within the border.
Season with salt and pepper, and sprinkle with chives if using.
Fold the edges of the dough over the filling, pleating as necessary to create a rustic look.
Bake for 25-30 minutes, or until the crust is golden brown and the eggs are set to your liking.
Let cool for a few minutes before slicing and serving.