To make the tart dough, in a mixer fitted with the paddle attachment, or a food processor fitted with the metal blade, beat the butter and sugar together until smooth. Add the egg yolks, vanilla and salt, then beat or process until blended. Add the flour, about 1/2 cup at a time. Mix until the dough begins to hold together as a cohesive mass. Dump the dough out of the machine and press it together into a rough ball. Place between two large sheets of plastic wrap and, working on an even surface, roll the dough about 1/8-inch thick. (You might find it easier to divide the dough in half, and roll each piece separately.) Slide a large baking sheet under the rolled-out dough and refrigerate for at least 1 hour, or overnight.
Remove the chilled dough from the refrigerator and let it sit at room temperature for a minute. Peel away the top sheet of plastic wrap. Cut the dough into 8 circles, each about 5 inches across. Press each circle of dough into a round tart pan about 4 inches in diameter. (If you don't have eight 4-inch tart pans, for individual servings, this amount of dough and filling can also be used to make two larger, 8-inch round tarts.) Trim off any dough that extends over the lip of the pans. Place the dough-lined tart pans in the freezer for 15 minutes, so the dough is thoroughly chilled before filling.
Preheat the oven to 350ºF. To make the walnut filling, using a heavy-duty mixer with a paddle attachment, or a hand-held electric mixer, beat the butter and brown sugar together until blended. Add the egg, Cognac, vanilla and salt, and beat until evenly mixed. Add the walnuts and beat vigorously until the mixture is blended; it will be quite thick. You will have about 3 cups. Spread about 1/3-cup of walnut filling in each tart shell. Bake about 20 minutes, or until the filling looks dry and slightly puffed. Remove from the oven to a wire rack to cool. When cool, remove each tart from its pan. To serve, place each tart on a plate and top with a scoop of ice cream (optional).