Preheat the oven to 350°F. Line a 8x8-inch pan with parchment paper.
To make the cookie: In the bowl of a stand mixer fitted with the paddle attachment add the butter, powdered sugar, and vanilla. Mix on low until combined. Add the flour and mix to combine completely.
Transfer the dough to the prepared pan and press it evenly into the pan with your hands.
Bake for 15 to 20 minutes or until it looks set slightly golden brown. When it comes out of the oven, use a spatula and flatten the sides and middle as it may rise just a little or you may not have flattened perfectly. By doing this immediately after it comes out of the oven will ensure an even cookie layer.
To make the caramel: In a small pot, add the cane sugar. Once the sugar on the bottom starts to melt, stir with a high heat spatula to keep from burning. The dry sugar will then sink to the bottom, so it can melt. Sugar clumps will form until the sugar turns into a liquid.
Once the sugar has completely melted into a liquid, add the butter. Be careful because steam will rise up quickly. Stir rapidly until the mixture is combined.
Once the butter is completely combined, add in the cream a little at a time. Be careful, because the cream is colder than the sugar mixture so more steam will rise up quickly. Stir rapidly to combine completely when each amount of cream is added.
Pour the caramel over the top of the cookie base. Allow to set until the caramel has cooled completely or overnight. Or store in the fridge to speed up the process. (I prefer to do this so the caramel cuts easily and smoothly when cutting the bars.)
Cut the bars into 16 bars, cut in half, then cut each side into 8 bars.
Line a baking sheet with parchment paper or grease a cooling rack and place on top of a baking sheet (this can help the excess chocolate drip off).
To make the topping: In a microwave safe bowl or using a double boiler, melt the chocolate. If using a microwave be sure to only do 30 second intervals, stirring between each one, to prevent burning.
Dip each bar into the melted chocolate and place on the baking sheet or cooling rack so the excess choose can drop off. Continue to cover all the bars.
Place the bars in the freezer for a few minutes, until chocolate is set. Remove and drizzle the remaining chocolate on top. You can add to a piping bag or just drizzle with a spoon. Sprinkle with flakey sea salt (optional).
Store in a cool dry place or in the fridge for up to 1 week.