Preheat the oven to 325 degrees F (165 degrees C). Place a 9-inch metal pie dish into a deep baking pan; pour boiling water into the baking pan to reach about halfway up the sides of the pie dish to make a water bath.
Pour 1/2 cup sugar and 1 teaspoon water into a heavy saucepan over medium heat. Gently swirl mixture in the pan until sugar dissolves, melts, and turns into a golden-brown caramel syrup, about 10 minutes. Watch carefully, as sugar burns easily. Pour melted caramel into the warmed pie dish; gently tilt the dish to coat the bottom with caramel.
Whisk egg yolks, condensed milk, evaporated milk, remaining 1/4 cup sugar, and vanilla in a bowl until creamy and thoroughly combined. If mixture is foamy, skim foam off with a folded paper towel. Gently pour custard over caramel in the pie dish. Cover the baking pan with aluminum foil.
Bake in the preheated oven until custard is set but jiggles slightly when nudged, 45 minutes to 1 hour. Remove foil and place flan with the water bath in the refrigerator until chilled, about 2 hours.
Remove the pie dish from the water bath; run a knife around the edges of flan. Invert flan onto a rimmed serving platter to release custard; let caramel sauce flow over flan.