In a medium saucepan over medium heat, combine the 3/4 cup of granulated sugar and the 1/4 cup + 1 Tbsp of warm water. Stir gently until the sugar dissolves. Allow the mixture to simmer without stirring until it turns a deep amber color, about 8-10 minutes. Carefully pour the caramel into your baking dish, tilting it to coat the bottom evenly. Be cautious; the caramel will be extremely hot.
In a mixing bowl, add the softened cream cheese and 2 tablespoons of granulated sugar. Using a whisk or an electric mixer, blend until smooth. Add the eggs one at a time, mixing well after each addition. Then, pour in the sweetened condensed milk, evaporated milk, and vanilla extract. Blend until completely smooth and well combined.
Pour the custard mixture over the caramel in the baking dish. Preheat your oven to 350°F (175°C). Place the baking dish in a larger baking pan and fill the outer pan with hot water until it reaches halfway up the sides of the flan dish. Bake for about 50-60 minutes or until the flan is set but still slightly jiggly in the center. Remove from the oven and allow it to cool for 15 minutes before refrigerating for at least 4 hours, or overnight for the best results.
When ready to serve, run a knife around the edges of the flan to loosen it. Invert a serving plate over the baking dish and flip it to release the flan. The caramel will flow over the top, creating a beautiful sauce. Slice and enjoy!