In a deep saucepan over medium high heat, combine sugar, water and corn syrup. Stir until the sugar is dissolved and then swirl occasionally until the mixture reaches at least firm ball stage (250°F-265°F). If you'd like a deeper caramel flavor and are comfortable taking the mixture to higher temperatures and judging "doneness" by color, wait for the mixture to become a medium amber color.
Carefully and slowly add the milk mixture to the syrup mixture, it will bubble furiously and the temperature will reduce by 30-40 degrees. Depending on how high a temperature you reached in the previous step, some of the caramel may seize, don't worry, it will dissolve/melt back into the mixture as you continue.
Stir constantly until the mixture reaches 245°F-250° F. Remove from heat and quickly add vanilla and butter stirring until the butter is incorporated and the mixture is creamy. (Caramel removed from the heat right at 245°F will have the softest, creamiest texture, as you approach 250°F, you will get firmer, chewier caramels, but anywhere within this range is going to work)
2 ounce butter, 1 teaspoon vanilla bean paste
Immediately pour the caramel into the prepared pan, set aside to cool and set overnight.
Once set, remove from pan and cut into individual pieces (approximately 1x1 inch squares). Use a very sharp knife and oil the cutting edge to prevent the candy from sticking to the blade. Wrap individually in parchment paper and store in an air tight container (if you leave them unwrapped, keep a small space between the caramels and put parchment or wax paper between the layers to avoid the individual pieces sticking to each other)