Make the salted caramel sauce: Heat granulated sugar in a medium saucepan over medium heat, stirring constantly with a heat resistant rubber spatula. The sugar will form clumps and eventually melt into a thick brown, amber-colored liquid as you continue to stir. Be careful not to burn otherwise the caramel will taste bitter and be unusable.
Once the sugar is completely melted, immediately add the butter. Be careful in this step because the caramel will bubble rapidly when the butter is added. Stir the butter into the caramel until it is completely melted. If you notice the butter separating, remove from heat and vigorously stir to combine it again.
Carefully and slowly drizzle in the heavy cream while stirring. Since the heavy cream is colder than the caramel, the mixture will rapidly bubble when added. Allow the mixture to boil for about 1 minute then remove from heat and stir in the salt. Pour salted caramel into a large mixing bowl and allow to cool down for approximately 30 minutes before proceeding to the next step. The caramel will thicken as it cools.
Preheat oven to 350°F (177°C).
Add the corn syrup, vanilla extract, and eggs to the salted caramel mixture, and whisk until well combined. Add the pecans and stir until well coated.
Pour filling into crust and bake for 40-45 minutes. The way to tell if pecan pie is done is when the center gives you just a little jiggle—like the stable but slightly wiggly movement of Jell-O when you give it a gentle shake—but the edges are stable and set. Allow pie to cool before slicing & enjoying. Cover and store leftover pie at room temperature for 1-2 days or in the refrigerator for 4-5 days.