Combine the cream, sugar, butter and corn syrup in a large stock pot (at least 6+ quart).
Bring the mixture to a boil, stirring regularly. Be very careful not to leave the kitchen, the mixture can bubble over very quickly!
Cook over medium-high heat, stirring occasionally until the mixture reaches 245°-248°F (use a good quality candy thermometer). It can take up to 2 hours to reach this temperature. I usually bring a chair into the kitchen and just sit while waiting and watching (getting up to stir as needed).
While cooking the caramel, prepare a jelly roll pan (large rimmed baking sheet) by lining with parchment paper. You want the parchment to come up the sides of the pan, with an inch or two of overhang (so you can grab the paper and remove from the pan once the caramels have cooled).
Additionally, while cooking the caramel, preheat the oven to 300° to toast the pecans. Chop pecans first, then spread onto a baking sheet and bake in pre-heated oven for 3-5 minutes, or until fragrant. Remove from oven and set aside.
Once your caramel mixture has reached 245°F, remove the pan from the heat and stir in the 1 tablespoon of vanilla and 1 tablespoon of sea salt. Stir quickly to fully combine, then carefully pour the mixture into the prepared pan.
Top the warm caramel with an additional sprinkling of coarse sea salt, and the toasted pecans. Press the pecans in just a bit if needed.
Move the caramels to a cool (indoor) location out of the way and allow to cool for 8 hours. Cover the pan loosely with foil (careful not to have the foil lying directly on the caramel) or use a jelly roll pan lid if you have one.
Once fully cool and set, pick up the edges of the parchment paper to move the caramel slab to a cutting board. Peel back the parchment paper, and use a sharp knife to cut the caramels into small squares or rectangles.
Individually wrap the caramels in parchment or cello wrappers, then store in an airtight container, at room temperature, for up to 2 weeks.