Lightly grease an 8x8-inch square pan and line with parchment paper (the baking spray helps keep the parchment in place). Set aside.
In a large glass measuring cup, add the cream, butter and salt. Microwave on high in 30-second intervals until cream is hot and steamy and the butter is melted, stirring or swirling gently between microwave intervals. Set aside.
In a large heavy-bottomed pot (I used my 3-quart dutch oven - you want a large pot for this as the mixture boils up quite a bit), add the sugars, corn syrup and water. Whisk until thick and grainy. Use a wet pastry brush to wipe down the inside of the pot. Clip your candy thermometer to the side of the pot, making sure the tip is submerged but not touching the bottom of the pot.
Turn the heat to medium. Without stirring, heat to 260 degrees. Remove from heat, then slowly whisk in the cream mixture. Mixture will boil up.
Return to heat and, again without stirring, heat to 250 degrees. Turn off heat, quickly but gently whisk in the vanilla, and carefully pour into the prepared pan. Do not scrape the bottom of the pot, as this will have burned sugar that you do not want in your caramels.
Top caramels lightly with coarse sea salt and allow to cool completely, at least 2-3 hours or, preferably, overnight. Cut into squares or rectangles and wrap each piece in waxed paper.