Prepare the Caramel Sauce: In a medium saucepan over medium heat, combine the sugar and water. Stir until the sugar is completely dissolved. Let it cook without stirring until it turns a deep amber color. Carefully whisk in the sea salt and heavy cream—it will bubble up vigorously, so be cautious. Continue whisking until smooth. Remove from heat and stir in the butter and vanilla extract. Allow it to cool.
Make the Cream Cheese Filling: In a large mixing bowl, beat the softened cream cheese and granulated sugar until smooth and creamy. Add the heavy cream and vanilla extract, and continue to beat until fluffy and well combined.
Assemble the Cake: Line an 8×8-inch baking dish with plastic wrap, leaving enough overhang on the sides for easy removal later. Place a layer of 16 Ritz crackers on the bottom of the dish. Spread 1/3 of the cream cheese mixture over the crackers, then drizzle with 1/3 of the caramel sauce. Repeat the layers two more times, finishing with the cream cheese mixture on top.
Chill the Cake: Cover the dish with plastic wrap and refrigerate for at least 12 hours, or overnight, to let the flavors meld and the cake set.
Serve: Use the plastic wrap to lift the cake out of the dish. Cut into squares and serve with a dollop of whipped cream and a drizzle of extra caramel sauce.
