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1. Preheat the oven to 350u00b0F/180u00b0C, and place one rack in the center and one rack in the top third of the oven. Line the baking sheets with parchment paper.
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2. Shape the brioche dough into a rectangle about 8 in/20 cm long, 4 in/10 cm wide, and 1 in/2.5 cm thick. Using a ruler and a knife, cut the rectangle into eight 2-in/5-cm squares by first dividing it in half horizontally and then dividing it vertically into strips 2 in/5 cm wide. Each square of dough should weigh about 3 1/2 oz/100 g. Stretch each square into a circle about 5 in/12 cm in diameter as if you are making a small pizza. Stretch the inner part of the circle so that it is quite thin and shape the edge of the circle to create a rim. The center should be almost paper-thin, and the finished circle should look like you are making the crust for a mini deep-dish pizza. Place the brioche circle on one of the prepared baking sheets and repeat with the remaining dough squares, spacing them 2 to 3 in/5 to 7.5 cm apart and using both baking sheets.
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3. Using the back of a spoon, spread 1 tbsp of the creme fraiche over the base of each brioche circle, spreading it evenly over the base but leaving the rim bare. Cut the bacon slices in half. For each pizza, press three half slices of bacon against the brioche rim to create a bacon wall. Divide the caramelized onions evenly among the pizzas, spooning and spreading the onions next to the bacon and leaving the center of the circle bare except for the creme fraiche.
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4. Bake the pizzas, switching the baking sheets between the racks and rotating them back to front about halfway during baking, for about 15 minutes, or until the edges of the pizza start to turn light brown. Remove the baking sheets from the oven and carefully crack an egg into the center of each pizza. Sprinkle about 1/4 cup/30 g of the mozzarella on top of each pizza, covering both the egg and the exposed rim of brioche. Bake for another 8 to 10 minutes, again switching the baking sheets between racks and rotating them back to front about halfway during baking, or until the cheese has melted, the edges of the egg are cooked but the yolk is still wiggly, and the edges of the pizza are golden brown. Remove from the oven. Let the pizzas cool for 8 to 10 minutes to allow the eggs to set up a bit before serving.
