Butter two 8" x 8" or 10 1/2" x 6 1/2" pans. Measure the vanilla into a small container, and set it aside for later.

Cut the butter into 1" chunks, to help it melt faster. Combine the cut-up butter, half & half, corn syrup, sugars, and salt in a heavy-bottom, 5- to 6-quart saucepan.

Heat the mixture over medium-low heat until everything has melted, stirring constantly. Attach a candy thermometer to the side of the pan.

Cook slowly, stirring constantly, until the mixture reaches 248°F, or until a small amount dropped in cold water forms a firm ball. As the mixture boils it will become thicker and thicker and the frothy bubbles will give way to a more blurpy bubble that resembles thick lava. This happens gradually, but you'll notice it around 230°F and higher. This is when you really have to pay attention and watch the temperature carefully, as it tends to move more quickly from 230°F up. The whole process will take about 2 hours. Perfect your technique Blog Mom's Caramels By Barb Alpern

Remove the pan from the heat, and carefully stir in the vanilla; the mixture will bubble and boil.

Quickly pour the caramel into the prepared pans. Don't add any residue from the pot into the pans; instead, scrape it into a separate container. Baker's treat!

Wait 30 minutes, then sprinkle with coarse-flake sea salt, if desired.

Cover the candy securely, and refrigerate.

Remove the candy from the pan by loosening its edges with a knife or offset spatula, and banging the pan on a cutting board until the slab releases from the pan. Allow the candy to warm up a bit if it's hard, or it'll shatter when you bang the pan.