To a medium saucepan, add the sugar and ¼ cup of water. Cook over medium heat, stirring frequently, for about 2 minutes, or until the sugar is dissolved.
Increase the heat to medium-high and cook, swirling occasionally, for about 5 minutes until golden or amber in color. (If sugar crystals form on the side of the pan, use a wet pastry brush to push them down the sides.)
Immediately pour the caramel into an 8-inch round cake pan. Tilt and turn the pan to spread the caramel out to the edges, then set the pan aside to cool and harden while you make the custard. (Be careful- the bottom of the pan will be very hot!)
Combine the eggs, condensed milk, evaporated milk, and vanilla extract in a blender or a large mixing bowl. If blending, blend on low just until combined, and set aside for a few minutes to let any bubbles on the surface settle. If using a mixing bowl, whisk it together until well combined. If the milk mixture if too bubbly in either method, pour it through a fine mesh sieve into to the pan to remove the air bubbles.
Place the pan with the caramel in a roasting pan. Pour the milk mixture directly into the pan over the hardened caramel. Fill the roasting pan with 1 inch of hot water.
Bake for 35 to 40 minutes until the center is just set. (It will wobble slightly when you jiggle the pan but continue to set as it cools.)
Remove the cake pan from the roasting pan. Transfer it to a wire rack and allow it to cool to room temperature before serving. (You can refrigerate the flan if you prefer as well.)
To serve, run a small sharp knife around the edge of the pan then place a serving dish upside down on top. Flip and remove the pan. (If you chilled the flan, dip the pan halfway into a bowl of hot water to warm the caramel before inverting onto a plate.) Slice and serve.
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Notes
When making the caramel: If sugar crystals form on the side of the pan, use a wet pastry brush to push them down the sides.
Keep an eye on the caramel. It can burn very quickly, so watch it closely. Use a light-colored pot as well to help determine how dark the caramel is. You want it to be a deep golden brown. Lighter caramel will lend less flavor to the baked flan.
For a perfectly smooth flan: After blending, strain the mixture through a fine mesh strainer directly over top of the hardened caramel in the cake pan. This is an easy way to remove any remaining bubbles as well!
To remove air bubbles in the custard: Gently tap the cake pan on your counter to help any air bubbles inside the custard escape.
For neat slices: Use a sharp knife and wipe it off between each slice.