Line a 9x13-inch baking dish with foil or parchment paper. Use a lot of butter to grease the foil or paper. Leave the food alone.
Heavy brown sugar, light brown sugar, powdered sugar, and light corn syrup should all be put into a Dutch oven or medium to large pot.
In a pan set over medium-low heat, stir the sugars all the time for about 10 minutes, or until they melt.
When it starts to boil, add the heavy cream very, very slowly. Slowly, add about a teaspoon at a time, and stir the mixture all the time.
It should be boiling the whole time. It might take 20 to 30 minutes to add all the cream in this step.
Keep boiling the mixture and stirring it all the time. While you do this, scrape the pot's bottom and sides until the mixture reaches 240 to 245°F. For this, I like to use a candy thermometer.
Take it off the heat and add the vanilla. Pour the caramel right away into the baking dish that has been prepped. Leave it out in the open until it's completely cool.
Put in the fridge for 4 to 6 hours, or better yet, overnight, until it hardens. Lift the foil or parchment paper off the dish to get the caramels out.
Then cut them up into little pieces. Put a lot of sea salt on top and serve right away.