Preheat oven to 400 degrees F. Bring chicken broth to a boil over high heat with reserved fennel stalks and fronds and simmer until reduced by half.
On a lightly floured work surface with a floured rolling pin, roll out puff pastry to 1/8-inch thickness. Using an inverted two-cup ramekin or individual casserole, trace four circles from puff pastry dough with a sharp knife, creating a one-inch overhang. Place circles on a parchment-lined baking sheet, cover them with plastic wrap and chill.
In a heavy skillet, melt butter on medium-high and add chopped fennel fronds, reserved chopped fennel stalks and shallot and white wine. Cook, stirring, for two minutes, then reduce heat and continue cooking, stirring occasionally, about seven minutes. Add sliced mushrooms and continue cooking and stirring until fennel and mushrooms are tender, about two minutes. Add herbs if using and salmon pieces, stir to combine and reserve.
Mix cornstarch and milk together until cornstarch is dissolved. Whisk milk mixture into simmering broth and continue whisking until liquids are incorporated and mixture thickens into gravy. Continue cooking, stirring constantly, an additional two minutes to cook starch. Season with salt and pepper to taste. Stir one and a half cups gravy into salmon-fennel mixture.
Assembly: Butter four individual two-cup ramekins. Distribute salmon mixture evenly in the ramekins, but do not over-fill. Spoon in some additional gravy and put a pat of remaining butter in each ramekin. Top each with a pastry circle, curling the edges of the overhang upward and pressing gently just inside the lip of the ramekin to adhere pastry. Place ramekins on a baking sheet in preheated oven and bake until golden brown and bubbly, about 15 minutes.