In a heavy saucepan, melt the butter over medium-high heat. Add the mushrooms and cook, stirring, until wilted and golden brown around the edges, about 5 minutes. Add the shallots and cook until softened, about 1 minute. Add the cognac and cook until almost completely evaporated. Sprinkle the flour over the top of the mushrooms and shallots, stir to combine well, and cook for 2 minutes. Add the shrimp stock and milk, and whisk until smooth. Continue to cook until thickened. Add the heavy cream, green peas, salt, nutmeg, cayenne pepper, and thyme, and cook for 15 minutes, until sauce is thick enough to coat the back of a spoon and the flavors have come together. Set aside until cooled. Add the lobster meat, chives, and tarragon. Refrigerate until thoroughly chilled, then divide lobster mixture evenly among four 12-ounce ramekins.

Preheat the oven to 400 degrees F.

On a lightly floured work surface, roll puff pastry to a thickness of 1/8-inch. Using a decorative cutter, cut the pastry into circles 3/4-inch larger than the diameter of the ramekins. Transfer the dough rounds to the top of the ramekins and press the edges of the pastry around the top of the dishes. With a pastry brush, lightly coat the top of the pastry with some of the egg yolk mixture. Using the tip of a paring knife, cut a slits in the center of the pastry for the steam to escape.

Bake in the middle of the oven for 20 to 25 minutes, or until pastry is puffed and golden brown and sauce is bubbling hot.