1. Preheat oven to 350°F (175°C).
2. In a mixing bowl, combine flour, sugar, and salt. Cut in the cold butter until the mixture resembles coarse crumbs.
3. Add the beaten egg and mix until the dough comes together. Press the dough into a tart pan.
4. Bake the crust for 15 minutes. Remove from oven and let cool.
5. In a bowl, mix together the chopped walnuts, brown sugar, corn syrup, heavy cream, melted butter, and vanilla extract.
6. Pour the filling into the cooled crust.
7. Bake for 30 minutes or until the filling is set.
8. Let the tart cool before serving.