- Preheat the oven to 350°F. Grease and line an 8 inch square pan with parchment paper so that the paper comes up the sides of the pan.
- Stir the flour, sugar and salt together. Cut into the butter until the mixture is a rough crumbly texture (it should not come together as a dough). Press this into the bottom of the prepared pan and bake for about 15 minutes, until it just begins to brown at the edges. Allow to cool while preparing the filling.
- Bring the sugar, cream of tartar and water into a small sauce pot and boil on high heat, uncovered and without stirring, occasionally brushing the sides of the pot with water until the sugar caramelizes, about four minutes. Remove the pot from the heat and whisk in the cream and butter, watching out for the steam. If the sugar sticks to the whisk or pot, return the pot to low heat and stir until evenly melted. Allow the caramel to cool for 10 minutes.
- Whisk the egg in a medium bowl, then whisk in the brown sugar and vanilla. Whisk in the caramel and then stir in the walnut pieces. Pour this mixture into the prepared pan and spread the walnut evenly. Bake for 20 minutes, until the outside edges are bubbling. Cool the squares to room temperature before slicing.
The squares can be stored in an airtight container for up to six days.