1. In a 1 1/2- to 2-quart pan, bring chicken broth and rice to a boil over medium-high heat. Reduce heat, cover, and simmer until rice is tender to bite, about 15 minutes.
2. Meanwhile, in a 2- to 3-quart pan over medium heat, melt butter. Add onion and mushrooms and stir often until onion is soft and liquid has evaporated, 7 to 8 minutes. Add wine, increase heat, and bring to a boil; add salmon chunks and reduce heat to maintain a simmer. Cook, stirring often, until salmon is broken into flakes and most of the liquid has evaporated, 7 to 10 minutes. Stir in rice, salt, pepper, and herbs.
3. Cut each puff pastry sheet into nine 3-inch squares. On a lightly floured work surface, with a lightly floured rolling pin, roll each square once in each direction to flatten and stretch to approximately 4 inches. Place 1 tablespoon filling in the middle of each square. Brush edges lightly with egg mixture and fold diagonally over filling to make triangles; pinch edges to seal. Arrange pastries 1/2 inch apart on two cooking parchment-lined 12- by 15-inch baking sheets. Lightly brush the top of each pastry with egg mixture.
4. Bake pastries in a 375° regular or convection oven until golden brown, 20 to 25 minutes. Serve warm.
Nutritional analysis per pastry.