In a saucepan over medium heat, combine the blueberry pomegranate preserves, rosemary, and 1 tbsp butter. Simmer for 5-10 minutes, stirring occasionally. Remove from heat and allow to cool.
Meanwhile, heat a non-stick skillet on medium-high heat with 1 tbsp of butter. Crack the eggs into the pan and fry until the white part has set, about 3-5 minutes.
Place one slice of cheese on the bottom half of each croissant. Place the croissants in the toaster for 2-3 minutes, just enough to melt the cheese.
Spoon the preserves over the cheese, then add the bacon and fried egg. Place the top half of the croissant over the sandwich and enjoy!