Special equipment: a 2 1/2-inch round cookie cutter
For the biscuits: Position an oven rack in the center of the oven, and preheat to 425 degrees F. Line a baking sheet with parchment.
Whisk together the flour, chives, baking powder, sugar and salt in a large bowl. Add the goat cheese, and toss, using your hands to break it up into pea-sized pieces. Add the cream, and mix with a wooden spoon until combined. Let the dough stand for 5 minutes.
Roll the dough out into a round that is slightly less than 1/2 inch thick. Cut out 8 biscuits with a 2 1/2-inch round cookie cutter, and arrange them about 2 inches apart on the prepared baking sheet. Brush them with more cream, and sprinkle with a little salt. Bake the biscuits until just golden, 16 to 18 minutes. Transfer them to a wire rack, and let cool. When the biscuits are cool enough to handle, split them in half. Put 2 bottom halves on each of 4 plates.
For the quick hollandaise: Whisk the mayonnaise, lemon juice, paprika and 1 tablespoon water in a small bowl, and season with salt and pepper; set aside.
Heat a large nonstick skillet over medium-high heat. Cook the bacon in batches until browned, 3 to 4 minutes per side. Place 1 slice of bacon on each biscuit bottom, folding if needed.
Bring a wide pot with about 2 inches of water to a very gentle simmer. Break the eggs into the water, spacing them apart. Cover the pot, and turn off the heat. After 2 to 3 minutes the whites should be set and the yolks still soft. Remove the eggs with a slotted spoon, and place on top of the Canadian bacon slices. Drizzle with hollandaise, sprinkle with chives and sandwich each with a biscuit top.
Never leave a child unattended in the kitchen. Limit the child to tasks that are safe and age-appropriate.
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