Preheat oven to 425°F.
In a 10-inch skillet over medium heat, cook chopped bacon until it is mostly cooked but not crisp. Place the cooked bacon on paper towels to drain excess grease. Remove all but approximately 1 tablespoon of bacon grease from the skillet and lower the heat to medium-low.
Add the mushroom and shallots to the skillet and cook and stir until tender (about 5-7 minutes.)
Remove from heat and stir in cheeses, salt, and pepper. Set aside.
On a lightly floured surface roll puff pastry into a 10 by 9-inch rectangle. Transfer to a parchment-lined cooking or baking sheet. Note: if using store-bought puff pastry unfold it before rolling it out.
Create a border by scoring the puff pastry with a knife an inch from the edges, being careful to not cut all the way through it. Dock the pastry by poking holes with a fork in the center area.
Beat 1 egg and water; brush over pastry edges. Refrigerate the pastry for 10 minutes.
Spread mushroom, shallot, and cheese mixture over the center of the pastry to within 1 inch of the edge. Top with bacon and bake for 10-12 minutes or until the pastry has puffed and is golden brown.
Remove from the oven and carefully crack the eggs over the tart leaving space between each egg. Bake until the eggs whites are set, about 4-6 minutes.
Remove from oven and sprinkle with parsley. Cut into four slices and serve immediately.