Preheat the oven to 375 degrees F. Place a skillet over medium heat. Melt 2 tablespoons butter and then add chopped onion. Saute for 5 minutes until the onion is translucent. Add the mushrooms and cook for 10 to 15 minutes until the mushrooms are brown. Season with salt and pepper and remove from the heat. Let cool completely.
Melt the remaining butter in a skillet over medium heat. Add the sliced charred or spinach and cook stirring for one minute. Season with a pinch of salt. Then add ¼ cup of water, cover the skillet with a lid, and lower the heat to medium-low. Cook covered until the chard is soft but still green and vibrant, for about 5 minutes. Transfer to a mesh sieve and press with a back of a spoon to drain the excess liquid. Set aside.
In a small bowl mix rice and chopped dill. Season to taste with salt and pepper.
Place one sheet of puff pastry on the baking sheet lined with parchment paper. Top it with cooked rice, make sure to leave 1 ½ inch border around the edges.
Layer the spinach over the rice. Follow with fried mushrooms. Top with a salmon filet and sliced egg. Season with black pepper.
Cover everything with the second sheet of puff pastry and carefully roll in the edges.
Whisk the egg and brush the coulibiac. Top with caraway seed or sesame seeds.
Bake for 35 minutes until the pastry is golden.