Place 1/2 cup granulated sugar and 2 tablespoons water in a small heavy saucepan over medium heat. Swirl the pan gently (do not stir) as the sugar dissolves and begins to caramelize. When the sugar reaches a deep amber color (about 6–8 minutes), quickly tilt the pan and carefully pour the caramel into six 6-ounce ramekins or a 9-inch pie dish, swirling each ramekin to coat the bottom evenly. If the caramel begins to thicken before coating, add up to 1 teaspoon hot water to loosen briefly, then pour. Set ramekins aside to let caramel harden.

Custard

Preheat and prepare a water bath

Preheat oven to 325°F (160°C). Arrange a large roasting pan on the middle rack where the filled ramekins will sit so you can assemble the water bath easily.

Warm the dairy

In a medium saucepan, combine 2 cups whole milk and 1/2 cup heavy cream. Warm over medium heat until just steaming and small bubbles form around the edge (do not boil), about 5 minutes. Remove from heat.

Bloom espresso

If using instant espresso powder, stir 1 teaspoon into a tablespoon of the warm milk until dissolved; if using brewed espresso, stir it into the warm milk now.

Whisk eggs and sugar

In a large bowl, whisk together 4 whole eggs, 2 egg yolks, and 1/2 cup granulated sugar until combined and slightly frothy, about 30 seconds. Add 1/4 teaspoon fine salt.

Temper and flavor

Slowly pour the warm milk mixture into the egg mixture in a thin stream while whisking constantly to temper the eggs. Stir in 2 tablespoons coffee liqueur and 1 teaspoon vanilla extract. Strain the custard through a fine-mesh sieve into a clean bowl or measuring cup to remove any cooked egg bits and ensure a silky texture.

Fill ramekins

Place the caramel-lined ramekins in the prepared roasting pan. Carefully pour the strained custard into each ramekin, filling to about 1/4 inch below the rim (leave a little room for expansion).

Bake in a water bath

Pour hot (not boiling) water into the roasting pan until it reaches halfway up the sides of the ramekins. Cover the roasting pan loosely with foil to minimize cracking and steam loss. Bake at 325°F (160°C) until custards are set but still slightly jiggly in the center, about 35–45 minutes (start checking at 30 minutes). A thin knife inserted near the center should come out mostly clean.

Cool and chill

Carefully remove ramekins from the water bath and cool on a wire rack until room temperature, about 30–45 minutes. Then refrigerate uncovered for at least 4 hours or up to 24 hours to fully set and develop flavor.

Finish & Serve

Unmold and glaze

To unmold, run a thin knife around the edge of each ramekin to loosen the custard. Place a small plate over the ramekin and invert quickly. The caramel will flow over the custard forming a glossy glaze. If any caramel sticks, loosen and pour again.

Optional garnish

Top with a dollop of whipped cream and a few fresh berries or shaved chocolate if desired. Serve chilled.