Stir together sugar and ¼ cup water in a medium heavy saucepan until sugar is completely moistened. Bring to a boil over medium heat, 3-5 minutes, and cook, without stirring, until mixture begins to turn golden, another 1 to 2 minutes.

Gently swirl the pan, continue to cook until sugar is the color of peanut butter, 1 to 2 minutes.

Remove from heat and swirl until sugar is reddish-amber and fragrant.

Carefully swirl 2 tablespoons of warm tap water into the pot. The mixture will bubble and steam.

Pour this caramel into 8 ½ by 4 ½ inch loaf pan, but do not scrape out the sauce pan.

Set the loaf pan aside.

Adjust oven rack to middle position and heat oven to 300 degrees F.

Line the bottom of a 13 by 9 inch baking pan with dish towel, folding the towel to fit in well, and set aside.

In a large bowl, whisk the eggs and yolks until combined. Add sweetened condensed milk, evaporated milk, whole milk, vanilla, and salt and whisk until incorporated.

Strain the mixture through a fine mesh strainer into the loaf pan that has the caramel in it.

Cover loaf pan tightly with aluminum foil and place in the prepared towel lined baking pan.

Turn oven down to 180 degrees F and bake flan at 180 degrees F, 1 to 1 ½ hours.

Remove foil and leave custard in a water bath until the loaf pan has cooled completely. Remove loaf pan from water bath, wrap tightly and chill overnight or up to 4 days.