Preheat your oven to 325 degrees Fahrenheit. In a medium bowl, combine the graham cracker crumbs, melted butter, and sugar. Mix until the texture resembles wet sand. Press the mixture firmly into the bottom and one inch up the sides of a 9 inch springform pan. Bake the crust for 10 minutes, then set it aside to cool completely while you prepare the filling.
In a large mixing bowl, beat the softened cream cheese and one cup of sugar on medium speed until the mixture is completely smooth and fluffy. This usually takes about three to four minutes. Be sure to scrape down the sides of the bowl with a spatula to ensure no lumps remain before moving to the next step.
Reduce the mixer speed to low and add the sour cream and alcohol-free vanilla extract. Mix until just combined. Add the eggs one at a time, beating briefly after each addition. It is important not to overmix the batter at this stage, as too much air can cause the cheesecake to puff up and then crack as it cools.
Pour the batter over the cooled crust. If you want a very smooth top, you can place the springform pan inside a larger roasting pan and fill the roasting pan with one inch of hot water to create a water bath. Bake for 65 to 75 minutes, or until the edges are set but the center still has a slight jiggle. Turn off the oven and leave the door cracked for one hour to allow the cake to cool slowly.
In a small saucepan over medium heat, combine the heavy cream, brown sugar, four tablespoons of butter, and sea salt. Bring the mixture to a gentle boil, stirring constantly. Once it begins to bubble, reduce the heat and simmer for about five minutes until the sauce thickens and coats the back of a spoon. Remove from heat and let it cool to room temperature.
Once the cheesecake has reached room temperature, refrigerate it for at least four hours, or preferably overnight. Before serving, drizzle the homemade caramel sauce generously over the top. Use a warm, sharp knife to slice the cheesecake for the cleanest presentation.
