In a saucepan over medium heat, combine 1 cup of sugar and 1 cup of water. Stir gently until the sugar dissolves. Stop stirring and allow the mixture to boil until it turns a deep amber color. Quickly pour the caramel into the bottom of your cake pan, tilting to coat the bottom evenly. Be careful, as the caramel will be extremely hot.
In a large mixing bowl, whisk together the 3 cups of whole milk, 4 whole eggs, 2 egg yolks, 1 cup of sugar, 1 teaspoon of salt, and 2 teaspoons of vanilla extract. Mix until fully combined and smooth.
Once the caramel has set (it will harden as it cools), carefully pour the custard mixture over the caramel in the cake pan.
Preheat your oven to 350°F (175°C). Place the cake pan in a roasting pan. Fill the roasting pan with hot tap water, enough to reach halfway up the sides of the cake pan. This water bath will help cook the flan evenly.
Carefully place the roasting pan in the preheated oven. Bake for about 50-60 minutes, or until the flan is set but still slightly jiggly in the center.
Once baked, remove the flan from the oven and let it cool in the water bath for about 30 minutes. Then, refrigerate for at least 4 hours or overnight for best results.
To serve, run a knife around the edges of the flan to loosen it. Invert onto a serving plate, allowing the caramel to drizzle over the top. Slice and enjoy your homemade flan!