Lightly toast walnut and pecan pieces in a 350 F oven for 12 minutes. Set aside to cool.
Line a baking sheet with parchment and grease lightly with vegetable oil.
In a bowl, place butter, vanilla and baking soda together (no need to blend) and set aside.
In a heavy-bottomed pot over high heat, bring sugar, corn syrup and 1/3 c water to a boil. While sugar cooks, brush sides of the pot, right next to the edge of the sugar, with cool water. Boil sugar until it turns a light amber colour, about 12 minutes. Remove pot from heat and stir in butter, vanilla and baking soda quickly with a wooden spoon (the baking soda will make it foamy). Stir in walnuts and pecans until coated and spoon mixture onto prepared baking sheet. Spread brittle out as much as you can.
Allow to cool completely at room temperature.
To serve brittle, crack into pieces. Store brittle between layers of plastic wrap or paper in an airtight container at room temperature.