Preheat oven to 200°C. Mix the feta cheese, heavy cream and pepper in a bowl and set aside.
Cut the tops of the brioche buns and scoop out the centres of the bottom part of the brioche buns. Fill the buns with the cheese mixture and sprinkle with chopped bacon and grated Gruyère cheese.
Cover the filled bottoms with the top half of the buns and bake for 6-7 minutes. Meanwhile, fry the eggs and when the brioche is ready, carefully place a fried egg on top of each bun.
For the potatoes
Boil potatoes for 15 minutes and drain. Cut the potatoes into 4 and place them on a baking sheet, season with salt and pepper, drizzle with balsamic cream and olive oil and bake in a preheated oven at 200°C for 10 minutes, until browned and slightly caramelized.
Place some arugula and a few cherry tomatoes on each plate and drizzle with balsamic cream. Add a side serving of caramelized potatoes and serve.