Preheat the oven to 350. Line a 9 x 13 baking dish with parchment or foil, and set aside.
In a large bowl, whisk together the butter, brown sugar, and sugar. Add the egg, egg yolk, and vanilla, and mix until smooth. Add the flour and instant pudding, and stir to form a thick dough.
Divide the dough in half, and press half of the dough into an even layer in the bottom of the prepared baking dish.
Place the caramels and half and half in a medium microwave safe bowl. Cook on high for one minute, stir, then cook at 50% power for one minute intervals, stirring in between, until melted and smooth. Pour the caramel over the layer of cookie dough in the baking dish, and sprinkle with sea salt if desired.
Roll the remaining cookie dough out to a 9 x 13 rectangle between two pieces of plastic wrap. Remove one side of the plastic wrap, place the dough on top of the caramel layer, then remove the remaining piece of plastic wrap.
Bake 30-35 minutes, or until golden brown on top. Remove and let cool completely before slicing and serving.