Preheat oven to 300º ( see instructions below )
For the Carmel
Stir together sugar and 1/4 cup water in medium heavy saucepan until sugar is completely moistened.
Bring to boil over medium-high heat, 3-5 minutes and cook without stirring until mixture begins to turn golden, another 1-2 minutes.
Gently swirling pan, continue to cook until sugar is color of peanut butter, 1-2 minutes.
Remove from heat and swirl pan until sugar is reddish-amber and fragrant, 15-20 seconds.
Carefully swirl in 2 Tbsp warm tap water until incorporated; mixture will bubble and steam.
Pour carmel into 8 1/2x 4 1/2" loaf pan; do not scrape out saucepan.
Set loaf pan aside.
Adjust oven rack to middle position and heat oven to 300º.
Line bottom of 14x9" baking pan with dish towel, folding towel to fit smoothly and set aside.
Bring 2 quarts water to a boil.
For the Flan
Whisk eggs and yolks in a large bowl until combined. Add sweetened condensed milk, evaporated milk, whole milk, vanilla and salt and whistk until incorporated.
Strain mixture through fine-mesh strainer into prepared loaf pan.
Cover loaf pan tightly with foil and place in prepared baking pan. Place baking pan in oven and carefully pour all of boilinb water into pan.
Bake until center of custard jiggles slightly when shaken and custard registers 180º. 1 1/4-1 1/2 hours.
Remove foil and leave custard in water bath until loaf pan has cooled completely.
Remove loaf pan from water bath, wrap tightly with plastic wrap and chill overnight or up to 4 days.
To untold, slide paring knife around the edges of the pan.
Invert serving platter on top of pan and turn pan and platter over.
When flan is released, remove loaf pan.
Using rubber spatula, scrape residual caramel onto flan. Slice and serve.