Combine the brown sugar and 3 tablespoons bourbon in a small bowl or pie plate. Add the bacon and turn to coat. Let stand for 30 minutes.

Preheat the oven to 350°. Line a rimmed baking sheet with foil. Remove the bacon from the bourbon mixture and lay the strips on the foil, leaving a little room between the strips. Bake for 20–30 minutes, until browned but not too crisp. Remove from the oven.

Place the butter in a microwave-safe bowl. Microwave on high for 30 seconds. Remove from the microwave and stir. If the butter isn’t melted, microwave it for 30 seconds again. Remove it from the microwave and let it stand a few minutes.

Whisk in the egg yolks, lemon juice, and cream. Return to the microwave and cook on high for 1 minute, whisking every 20 seconds. Remove from the microwave and whisk in the mustard and the remaining 2 tablespoons bourbon. Add salt if needed. The sauce can be set aside for up to 1 hour or refrigerated overnight.

Add about 1 1⁄2 inches of water to a heavy skillet and bring to a boil. Reduce the heat to maintain a slow simmer. Carefully crack each egg into the water, swirling the water a little to bring the whites toward the yolk to create a compact shape. Cook until the whites are set but the yolks are still soft. Turn off the heat.

Toast the muffin halves. Microwave the hollandaise for 30 seconds to rewarm it if needed. (If it’s refrigerated, you may need to microwave it for 1 minute.)

Place a muffin half on a small plate and add about 1 tablespoon hollandaise. Cut 1 slice of bacon into 2 pieces and place the pieces on the muffin half. Remove a poached egg from the hot water with a slotted spoon and pat it dry around the edges with a paper towel. Place it on the bacon, then ladle more of the hollandaise over the top.

Repeat with the remaining bacon, muffin halves, and poached eggs. Serve immediately.