Special equipment: six 4-inch tart tins
For the pastry: Pulse the flour, hazelnuts, sugar and salt in a food processor to combine. Add the butter and pulse until coarse and crumb-like. Add 1 tablespoon water and pulse until the dough starts to form a ball. If the dough is too dry, add more water, 1 teaspoon at a time. Turn out the dough onto a work surface and form into a disc. Wrap in plastic wrap and chill in the refrigerator until firm, at least 1 hour.
Preheat the oven to 350 degrees F. Lightly butter six 4-inch tart tins.
On a generously floured work surface, roll the dough into a rough circle, about 1/8-inch thick. Make sure to work quickly, as the dough is easiest to work with while cold. Cut out three 6-inch circles. Gather the remaining scraps into a disc, roll out again, and cut three more circles. Line the tart tins with the circles, being careful not to stretch the dough, as it will shrink when baked. Roll a rolling pin over each tin to trim excess dough. Place the tins in the refrigerator to chill while you make the filling.
For the filling: Whisk together the sugar and eggs with an electric mixer on medium-high speed until pale and fluffy, about 2 minutes. With a spatula, fold in the walnuts and melted butter. Divide the filling among the chilled tart shells. Place the tins on a baking sheet and bake until the filling is golden brown and the crust is cooked through, 15 to 20 minutes. (If you find the tarts are browning too fast, cover them with aluminum foil while they finish baking.) Transfer to a wire rack to cool slightly while you make the sauce.
For the butterscotch sauce: Melt the brown sugar, cream and butter in a medium saucepan over medium heat. Stir with a wooden spoon until smooth. Once bubbling, let the sauce simmer, without stirring, for 3 minutes. Remove from the heat, add the walnuts, and stir until smooth. Let cool until just warm before serving.
To serve, remove the tarts from their tins and transfer to serving plates. Top each tart with a scoop of vanilla ice cream if using, and a drizzle of the butterscotch sauce.