This is a "flan loaf", from which you will slice and serve. Most flan recipes create individual servings.
Should be made the day before serving. We recommend an 8 1/2 by 4 1/2-inch loaf pan for this recipe. If your pan is 9 by 5 inches, begin checking for doneness at 1 hour and 15 minutes. You may substitute 2 percent milk for the whole milk if desired, but do not use skim milk. Select a platter with a raised rim for serving to contain the liquid caramel.
Stir together sugar and 1/4 cup water in medium heavy saucepan until sugar is completely moistened, then bring to boil.
Cook without stirring over medium-high heat 3 to 5 minutes, until mixture begins to turn golden, then another 1 to 2 minutes.
Gently swirling pan, continue to cook until sugar is color of peanut butter, another to 2 minutes.
Remove from heat and swirl pan until sugar is reddish-amber and fragrant, 15 to 20 seconds.
Carefully swirl in 2 tablespoons (1 oz) warm tap water until incorporated; mixture will bubble and steam.
Pour caramel into 8 1/2 by 4 1/2-inch loaf pan; do not scrape out saucepan. Set loaf pan aside to cool.
Preheat oven to 300°F and adjust oven rack to middle position.
Line bottom of 13" x 9" baking pan with dish towel, folding towel to fit smoothly, and set aside.
Bring 2 quarts water to boil.
Whisk eggs and yolks in large bowl until combined.
Add sweetened condensed milk, evaporated milk, whole milk, vanilla, salt, and optional espresso powder. Whisk until incorporated. Strain mixture through fine-mesh strainer into prepared loaf pan.
Cover loaf pan tightly with aluminum foil and place on top of the towel in the prepared baking pan. Carefully pour the boiling water into pan (bain-marie).
Place baking pan in oven and Bake until center of custard jiggles just slightly when shaken, and custard registers 180°F, ≈ 1¼ - 1½ 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. Chill overnight or up to 4 days.
To unmold, slide paring knife around edges of 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. Leftover flan may be covered loosely and refrigerated up to 4 days.