For the caramel sauce: In a large saucepan with tall sides (because the mixture will bubble), combine the sugar, corn syrup and 1/4 cup water. Heat over medium-low heat until the sugar dissolves, stirring occasionally. Increase the heat to medium-high and bring to a boil without stirring. Boil to a deep amber color, 5 to 6 minutes.
Remove the pan from the heat and whisk in the cream (be careful ¿ the caramel will bubble up vigorously!). Whisk in the vanilla, butter and salt. Let cool slightly, then transfer to a glass jar with a lid. (The caramel sauce will keep for 3 to 4 months in the refrigerator.)
For the candied pecans: Preheat the oven to 325 degrees F. Line a baking sheet with parchment paper, and spray with cooking spray.
In a medium bowl, add the corn syrup, sugar, salt, cinnamon, nutmeg and pepper; mix well. Add the pecans, stir to coat, and then transfer to a baking sheet. Bake for 5 minutes. Remove and stir the pecans. Return back to oven to finish cooking, another 10 minutes, or until the coating is bubbling. Remove from oven and use a fork to separate the cooked nuts on the baking sheet. Let cool.
For the ice cream: Whisk together the cream, condensed milk, vanilla and vanilla bean. Pour into the base of an ice cream maker and churn for 12 to 14 minutes; the mixture will double in size. Add the candied pecans; churn for 1 minute more.
Transfer one-third of the ice cream mixture into a shallow container, and drizzle with 1/4 cup of the caramel. Layer with another one-third of the mixture and 1/4 cup of the caramel sauce. Top with the remaining ice cream and another 1/4 cup of the caramel. (Reserve any extra caramel sauce for drizzling.) Cover and freeze until solid, at least 12 hours.
Before serving, let sit at room temperature for 5 minutes. The ice cream will keep in an airtight container in the freezer for up to 3 months.