Add sugar to a medium saucepan. Melt over medium-high heat and whisk as it melts. When it starts to clump up, keep whisking and it will eventually melt back down.
After all the sugar has melted, stop whisking and continue cooking. Keep the pan from burning by swirling it occasionally.
Cook the sugar until it turns amber in color, taking care not to leave it on too long once it begins to darken. At this point, it can easily burn.
Remove the pan from the heat and immediately add the butter, whisking it together. Whisk cream into the pan until combined. Allow to cool, then season with sea salt flakes.
For The Crust
Preheat the oven to 350 degrees Fahrenheit. Cover the bottom of your springform pan with aluminum foil if you plan to use a water bath and a springform pan.
In a mixer, cream coconut oil with sugar. Add vanilla and egg. Pour the remaining ingredients into the pan and spread evenly. Bake for 20-25 minutes or until golden brown. There will be some cooking left in the crust.
For The Cheesecake
Set the oven to 325°F. In a medium bowl, combine the cream cheese, brown sugar, vanilla, and salt. Mix at low speed until smooth, scraping the bottom and sides of the bowl occasionally.
Add the eggs one at a time, scraping the bowl between each addition. Add the caramel sauce and cream and stir well.
Fill the crust with the filling. When using a water bath, place your cheesecake pan inside a larger pan and fill the larger pan halfway with water. Bake for 60 to 80 minutes. It is a good idea to shake the cake gently until it is set around the edges and only 2" in the center jiggles.
Allow the cake to cool in the oven for an hour after turning off the oven. Place in the refrigerator until thoroughly chilled after removing from the oven.
For The Salted Caramel Mousse
Whisk the gelatin into the warm salted caramel mixture until it is completely dissolved, then set aside to soften for about a minute.
Mix the cream on high with an electric mixer until it reaches stiff peaks. Mix in the salted caramel mixture gently until combined.
Spread mousse over cheesecake. Caramelize the slices and drizzle them with them. Enjoy!