Preheat the oven to 425 degrees F. Line a baking sheet with parchment and spread the potato tots on the sheet. Bake until golden brown and crisp, about 25 minutes. Transfer the baking sheet to a wire rack and let cool. Lower the oven to 400 degrees F.
Meanwhile, heat the sausage in a large nonstick skillet over medium heat and cook, stirring to break up the sausage, until browned and no longer pink, about 8 minutes. Transfer the sausage to paper towels with a slotted spoon to drain; discard any remaining fat. Let the sausage cool, then crumble into 1/2-inch pieces.
Heat the bacon in the skillet over medium heat and cook, flipping once, until browned, about 8 minutes. Using tongs, transfer the bacon to paper towels to drain; discard any remaining fat. Let the bacon cool, then crumble into 1/2-inch pieces.
Prepare a bowl of ice water and set aside. Cover 4 eggs by 1 inch with water in a small saucepan and bring to a boil. Cover the pan, remove from the heat and let the eggs stand for 6 minutes. Uncover and drain the eggs, then transfer to the bowl of ice water and let stand for 3 minutes. Drain and peel the eggs, then quarter each egg lengthwise.
Toss the American cheese and Cheddar together in a small bowl until evenly combined.
Roll the dough into a 20-by-14-inch rectangle on a lightly floured work surface. Starting from the shorter end, spread the cheese mixture evenly over half of the dough, leaving a 1-inch border on the sides. Scatter the sausage, bacon and potato tots evenly over the cheese. Arrange all the egg quarters, yolk up, along the short side of the rectangle. Working from this short side, tightly roll the dough up, jelly roll-style, into a log. Pinch the open seams together to seal, then tuck them underneath the log.
Beat the remaining egg. Transfer the log to the prepared baking sheet and brush with the egg wash. Bake until the bread is golden brown all over, about 40 minutes.
Let the bread cool for 10 minutes. Halve the bread lengthwise, cut each half crosswise into 4 equal pieces and serve warm with ketchup or hot sauce.
To make rolling and shaping the dough easy, keep the dough refrigerated until 10 to 15 minutes before you are ready to use it.
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