For dough: Pour milk and half of sugar into a mixing bowl and stir together.
Sprinkle yeast over milk and sugar and allow mixture to sit for 4 to 5 minutes (yeast should begin to bubble and foam).
Stir in remaining sugar, salt, butter, egg, and herbs. Begin adding flour, ½ cup at a time, stirring to incorporate after each addition.
Once all the flour has been added, dump mixture onto a clean and lightly floured surface and knead dough for 5 to 7 minute or until smooth and elastic, adding more flour, 1 teaspoon at a time as needed.
Once smooth dough has formed, place dough into a lightly greasy bowl, cover with a clean, damp towel and place in a warm area until dough has doubled in size. About 1 hour.
For filling Melt butter into a skillet over medium heat. Add eggs, caramelized onions, and bacon and gently scramble together until about ½ cooked. Remove from heat and lightly season with salt and pepper. Allow mixture to cool.
To assemble: Once dough has doubled in size, punch down the center and turn onto a clean and lightly floured surface. Roll dough out into a 12”x 19” rectangle and about ¼″ thick.
Sprinkle half of the cheese over the surface of the dough and then gently spread the semi-cooked egg mixture over the cheese. Sprinkle the chives and remaining cheese evenly over the egg mixture.
Tightly and evenly roll the dough from one end to the other and gently pinch the seam shut. Place savory roll log seam side down and cut into 12 even rolls.
Lightly grease a 9”x12” baking dish with butter and line savory rolls into the dish. Loosely cover, place in a warm area and allow the rolls to proof again, for about 30 minutes.
Preheat oven to 375˚F.
Remove cover and bake savory rolls for 25 to 30 minutes or until golden brown on top.
For béarnaise: While the rolls cook, make the béarnaise. Place egg yolks and vinegar into a heatproof bowl and whisk together until the mixture doubles in volume. Place mixture over a pot with simmering water (make sure the water from the pot does not reach the bottom of your bowl) and begin whisking. While whisking, begin to add melted butter, in a slow and steady stream, until fully incorporated and the béarnaise is thick and smooth. (the sauce should gradually thicken as you add the butter) Remove from heat and add minced tarragon, the pinch of cayenne and season with salt and freshly cracked black pepper.