Fit pie shell dough into a 9-inch tart pan with a removable bottom. Preheat oven and bake tart shell according to package directions. Let shell cool completely.
Combine sugar, water, and corn syrup in a small, heavy saucepan. Bring to a boil over medium-high heat without stirring. Continue cooking without disturbing until mixture turns golden (about 15 minutes). Reduce heat to low, carefully drizzle in 3/4 cup cream and then stir until smooth. Stir pecans and vanilla extract into caramel mixture and then scrape into prepared tart shell. Chill for at least 30 minutes (or up to 2 days).
Place chocolate, remaining 1 Tbsp. cream and vegetable oil in a small microwavable bowl; heat mixture for 2 minutes at medium (50%) power. Stir until smooth. (If it doesn't melt after 2 minutes, microwave in additional 30-second intervals until smooth.)
Transfer chilled tart to a serving platter. Scrape melted chocolate into a corner of a small, sturdy plastic bag. Cut off top and drizzle chocolate on top of tart. Chill again until ready to serve.
For optional sweetened whipped cream:
Beat 1 cup heavy cream in a deep bowl with electric mixer on medium-high speed until in begins to thicken. Add 2 Tbsp. confectioners' sugar and 1/2 tsp. vanilla extract and beat just until cream forms soft peaks. (Yields about 2 1/4 cups)