Set out 4 (6-ounce) ramekins. To make the caramel sauce, combine 1 tablespoon sugar and 1 teaspoon water into each ramekin.
Microwave ramekins for 1-2 minutes in 25-second intervals, occasionally tilting and rotating the ramekins to mix the caramel sauce, until the caramel is golden brown.
Remove the ramekins from the microwave and immediately stir 1 teaspoon warm water into each before the caramel solidifies. (Use caution so as not to burn yourself, as the mixture will sizzle and sputter.) Set the ramekins aside so the caramel sauce can harden.
To make the custard, beat the eggs and sugar in a large bowl.
In a saucepan, combine the whole milk, heavy cream, salt, espresso powder, and vanilla. Bring to a simmer, then turn off the heat.
Vigorously stir the egg mixture while streaming the hot milk mixture into the bowl. Pour slowly so as not to curdle the eggs.
Strain the custard mixture through a sieve to ensure a silky texture. Set aside.
Place the ramekins in a deep, oven-safe pan set on top of a baking tray.
Pour custard into the ramekins.
Cover each ramekin with foil.
Prepare a bain-marie by adding hot water around the ramekins in the pan. The water should reach halfway up the sides of the ramekins.
Bake for 45 minutes to 1 hour, depending on the size of the ramekins. (If using 6-ounce ceramic ramekins, this should take about 1 hour.)
To check for doneness, remove a ramekin from the hot water bath and gently shake or tilt it. It should have a slight jiggle in the center, but be firm enough to cling to the edges of the ramekin.
Remove the ramekins from the water bath and let cool to room temperature before refrigerating for 3-4 hours.
To dislodge the purins, run a knife around the perimeter of the ramekins.
To serve, invert a ramekin onto a plate, shake firmly, and lift the ramekin. Enjoy.