Line a baking sheet with buttered parchment paper. In a medium saucepan, combine the sugar, water, corn syrup and butter and bring to a boil, stirring until the sugar is melted. Cook over moderate heat without stirring until the syrup reaches 270° on a candy thermometer, about 10 minutes. Stir in the chopped hazelnuts, salt, baking soda and vanilla and cook until the mixture is golden, about 3 minutes longer. Immediately pour the hot hazelnut brittle onto the prepared parchment and spread it in a thin layer using a spatula. Let the hazelnut brittle cool completely, then break into pieces.
The brittle can be stored in an airtight container at room temperature for up to 3 days.