In a small pan, heat up the syrup and rosemary. Let it steep for approximately 10 minutes. Remove the Rosemary and cool to room temperature.
Season and grill the Cheyenne Burger. Meanwhile whisk one egg with the cinnamon and milk. Dip the brioche bun into the mixture and toast both sides of the top and bottom bun in a sautée pan or at top.
Mix the peppered gravy with 1/8th cup of water and heat while whisking constantly. In another pan melt the butter and cook the other egg over medium. On the bottom of the “French toasted” bun add the Arcadian mix, then top with the burger, the sliced cheddar cheese and bacon. Top off with the peppered gravy and then the fried egg. - top off with the other “French toasted” bun and serve with a side of Rosemary syrup for dipping.