For the pizza: Preheat the oven to 450 degrees F. Line 2 baking sheets with parchment paper.
Place a large saute pan over medium heat. Add the bacon and onions. Cook, stirring occasionally, until the bacon fat has rendered and the onions soften, 8 to 10 minutes. Continue cooking, stirring frequently, until the bacon is crispy and the onions take on some color, about 6 minutes more. Remove from the pan with a slotted spoon and set aside.
To assemble the pizzas, lay the bread rounds on the prepared baking sheets. Divide the sour cream over each piece of bread, leaving a small rim exposed to serve as a crust. Divide the cheese and the bacon mixture over each piece. Sprinkle with salt and pepper.
Bake until crispy around the edges and the cheese melts, 8 to 10 minutes.
For the magic eggs: Place the shredded cabbage in a microwave-safe bowl with about 1 1/2 cups water. Cover with a damp paper towel and microwave for 2 to 3 minutes so the cabbage steams and releases its juice into the water, turning it purple.
Place 4 egg whites into 4 small bowls. Pour 1 tablespoon colored water into each egg white. Whisk vigorously (using a whisk, not a fork) to fully incorporate the water into the egg white. Watch the color change before your eyes! Place the saute pan used to cook the bacon over medium heat. Add the egg whites, keeping them separate, and cook until almost firm, about 2 minutes. Use a rubber spatula to release the sides of the egg whites from the pan. Place 1 egg yolk in the center of each egg white. Cook to desired doneness, about 1 minute more. Repeat with remaining egg.
Place 1 egg on top of each pizza. Sprinkle with the arugula and flakey sea salt. Slice into quarters and serve immediately.