In a medium saucepan, combine 1 cup granulated sugar and ¼ cup water. Cook over medium heat, stirring gently, until the sugar dissolves. Increase the heat to medium-high and cook without stirring until the mixture turns a deep amber color, about 10-12 minutes. Be careful not to burn the caramel.
Immediately pour the caramel into the bottom of a 9-inch round cake pan or a flan mold, tilting to evenly coat the bottom. Set aside to cool and harden.
Preheat your oven to 350°F (175°C).
In a large bowl, whisk together 1 can sweetened condensed milk, 1 can evaporated milk, 1 cup whole milk, 5 large eggs, and 1 tablespoon vanilla extract until smooth and well combined.
Pour the flan mixture through a fine-mesh sieve into the caramel-coated pan. This helps remove any egg solids and ensures a smooth custard.
Place the flan pan inside a larger baking dish. Carefully pour hot water into the larger baking dish to come halfway up the sides of the flan pan. This water bath (bain-marie) helps the flan cook evenly and prevents cracking.
Bake in the preheated oven for 60 minutes, or until the flan is set but still slightly jiggly in the center.
Remove the flan from the water bath and let it cool to room temperature. Cover and refrigerate for at least 4 hours, or overnight.
To unmold, run a knife around the edges of the flan to loosen it. Place a large serving plate over the flan pan and quickly invert to release the flan onto the plate, allowing the caramel to drizzle over the top.