In a mixing bowl, combine warm milk and half of the superfine sugar; sprinkle active-dry yeast over the top and let it foam for about 4-5 minutes. Mix in remaining sugar, salt, softened unsalted butter, egg, thyme, and chives, blending until combined, then gradually fold in all-purpose flour until a soft dough forms. Knead for 5-7 minutes until smooth, then let rise in a greased bowl for about 1 hour.

Melt unsalted butter in a skillet over medium heat. Add beaten eggs, caramelized onions, and crumbled bacon, scrambling until eggs are half cooked. Season lightly with salt and black pepper and allow filling to cool.

Once the dough has risen, punch it down and roll it out into a rectangle, about 1/2-inch thick. Sprinkle half of the shredded white cheddar across the dough, followed by the cooled egg mixture and chives. Add remaining cheese, then roll the dough into a log, cut into 12 pieces, and arrange in a greased baking dish. Let proof for 30 minutes.

Preheat oven to 375°F. Bake the rolls for 25-30 minutes, until golden brown on top. Remove and cool slightly.

For the Béarnaise sauce, whisk egg yolks and tarragon vinegar over simmering water until foamy. Stream in melted butter while whisking until thickened. Stir in minced tarragon, cayenne, salt, and black pepper.

Drizzle the Béarnaise sauce over the rolls or serve it on the side. Enjoy!