Step 1

Stir together water, yeast, and 1 teaspoon of the sugar in a small bowl; let stand until foamy, about 5 minutes.

Step 2

Combine yeast mixture, milk, eggs, 6 tablespoons of the butter, and remaining 2 tablespoons sugar in the bowl of an electric mixer fitted with a dough hook. Mix on low until well combined, about 10 seconds. While mixer is running on low, gradually add flour and 2 teaspoons of the salt until incorporated. Increase speed to medium, and continue beating until dough is smooth and elastic, about 4 minutes. Dough will be sticky. Transfer to a lightly greased large bowl. Cover with plastic wrap, and let rise in a warm place until doubled in volume, 1 to 1 1/2 hours.

Step 3

Meanwhile, cook bacon in a large skillet over medium, stirring occasionally, until crisp, 12 to 14 minutes. Using a slotted spoon, transfer bacon to a paper towel-lined plate. Pour drippings through a fine mesh strainer into a small bowl. Reserve drippings, discarding any solids. Wipe skillet clean; return 2 tablespoons of drippings to skillet over medium-low. Add onions, pepper, and remaining 1/2 teaspoon salt; stir to combine. Cover and cook, stirring occasionally, until onions are softened and beginning to brown, about 20 minutes. Uncover and cook, stirring occasionally, until onions are golden brown, 10 to 15 minutes. Transfer onions to a medium bowl and cool completely, about 30 minutes.

Step 4

Brush 18 muffin cups lightly with reserved bacon drippings. Turn dough out onto a lightly floured surface. Lightly flour top of dough; roll into an 18- x 14-inch rectangle. Spread onions in an even layer, leaving a 1-inch border on both long sides. Sprinkle bacon and Gruyère over onions. Starting with 1 long end, roll up dough, jelly-roll style. Using a serrated knife or dental floss, cut into 18 (1-inch-wide) pieces. Place pinwheels, cut side up, in prepared muffin tins. Cover loosely with plastic wrap; let stand in a warm place until increased in size, about 45 minutes.

Step 5

Preheat oven to 375°F. Remove plastic wrap, and bake in preheated oven until golden brown, 20 to 24 minutes. Meanwhile, stir together parsley and remaining 2 tablespoons butter. Brush butter mixture on hot rolls. Run a small offset spatula around edges of each pinwheel, and carefully transfer rolls to a wire rack. Serve warm, or cool completely, about 30 minutes.