In a small bowl, combine the walnuts, corn syrup, sugar, and salt. Spread in a single layer on a parchment lined baking sheet. Bake, stirring halfway through, until golden brown, about 7 minutes. Cool on a rack until crisp, about 5 minutes, and break into small clusters. (The nuts can be prepared up to 24 hours ahead; keep in an airtight container at room temperature.)
In a heavy-bottom 2-quart saucepan, cook the brown sugar, butter, and salt over medium heat, stirring until the sugar melts and begins to darken around the edges, about 5 minutes. Slowly whisk in the cream (some sugar will seize) and simmer, whisking occasionally, until smooth and thick enough that the whisk leaves the bottom of the pan visible, about 7-9 minutes. Whisk in the bourbon and simmer, whisking occasionally, until the whisk leaves the bottom of the pan visible again, about 1-2 minutes more. Stir in the vanilla. Transfer the caramel to a heat-proof measuring cup. Pour ⅓ cup of the caramel over the bottom of the cooled crust, spreading evenly. Refrigerate for at least 15 minutes to set the caramel. (Leave the remaining caramel at room temperature.)