Preheat the oven to 550°F or as high as it will go (if using a stone/steel, put it on a rack in the center or bottom third of the oven before you start preheating).
Cook the bacon in a medium skillet over medium heat until it's just beginning to crisp up, about 5 minutes. (Resist the urge to let it get crispy; it will cook more on the pizza!) Use a slotted spoon or skimmer to transfer the bacon to a paper towel–lined plate and set aside. Do not drain the grease in the skillet.
Stretch or roll out your dough to a 12-inch circle, then transfer it to an oiled baking sheet or a floured pizza peel (if using a baking stone/steel).
Brush the dough very lightly with the reserved bacon grease (don't worry about coating the dough; just give it a little sheen). Top with the cheese, and drizzle the cream evenly over the cheese.
Transfer the pizza to the oven and bake just until the crust turns golden and the cheese melts, about 5 minutes on a baking sheet or about 3 minutes on the baking stone/steel.
While the pizza bakes, crack the eggs into separate small ramekins or bowls. Make sure your salt and pepper are within arms reach of the oven.
Carefully pull out the oven rack. Slide the eggs onto the pizza, trying your best to place one in each quadrant of the pizza, and season with salt and pepper. Bake the pizza for another 3 to 5 minutes, until the egg whites are set but the yolks are still jiggly.
Take the pizza out of the oven. Sprinkle with the chopped chives. Slice and serve with hot sauce or any other condiments that make you happy.