In a mixer fitted with a paddle attachment, beat 10 tablespoons of the butter with the granulated sugar until creamy. Add 1 of the eggs, 1 teaspoon of the vanilla and the salt and beat until combined. Add the flour and mix well, then shape the dough into a flat disk, wrap in plastic wrap and chill for 1 hour.
In a medium saucepan over medium-high heat, bring the brown sugar, corn syrup and the remaining 3 tablespoons of butter and 1 teaspoon of the vanilla to a simmer. In a small bowl, whisk the remaining 2 eggs, then add a few tablespoons of the hot syrup to warm the eggs. Remove the syrup from the heat and whisk the warmed eggs into the syrup. Strain the filling into a bowl and chill for 1 hour.
Divide the chilled dough into 6 equal parts and roll out, 1 piece at a time, on a floured surface into 6-inch rounds. Press each piece of dough into a 4-inch tart pan (about 3/4 inch deep) or ring mold and trim around the rim. Refrigerate for at least 20 minutes. Preheat the oven to 350 degrees .
Divide the nuts and chocolate evenly among the unbaked tart shells and place them on a baking sheet. Pour in the filling and bake for 30 minutes. Cool the tarts on a rack for 10 to 15 minutes before removing them from the pans. Serve with vanilla ice cream.