Prepare coffee: Brew 120–150 ml strong espresso. Cool to room temperature, then refrigerate until needed. If using instant espresso powder, dissolve it in a couple of tablespoons of hot milk and set aside.
Warm dairy & dissolve sugars: In a medium heavy-bottomed saucepan combine whole milk and heavy cream. Add vanilla seeds/pod if using. Warm over medium-low heat to 75–80°C (170–176°F) — just below simmering. Whisk in granulated sugar and invert sugar (or corn syrup) until dissolved. Remove from heat briefly.
Whisk yolks: In a separate heatproof bowl whisk the 5 egg yolks until slightly thickened and pale.
Temper eggs: Slowly pour ~1/3 of the hot milk mixture into the yolks in a thin stream while whisking constantly to raise yolk temperature without scrambling.
Combine & cook custard: Return the tempered yolk mixture to the saucepan. Cook over low–medium heat, stirring constantly with a wooden spoon or heatproof spatula, until the custard thickens slightly and coats the back of the spoon. Use an instant-read thermometer and remove from heat at 78–82°C (172–180°F). Do not boil.
Strain & add coffee: Immediately strain the custard through a fine-mesh sieve into a clean bowl. Discard solids and vanilla pod. Stir in the chilled espresso, dissolved instant espresso (if used), salt, and coffee liqueur (if using) until fully incorporated.
Cool rapidly: Place the bowl in an ice bath and stir occasionally until the mixture reaches refrigerator temperature. Cover and refrigerate for at least 4 hours, ideally 8–24 hours (aging improves texture & flavor).
Churn: Pour the well-chilled base into your gelato or ice cream machine and churn according to manufacturer’s instructions until it reaches a dense, soft-serve consistency (generally ~20–30 minutes depending on machine).
Pack & harden briefly: Transfer gelato to a shallow airtight container, press parchment directly onto the surface to prevent ice crust, and freeze 1–4 hours until scoopable. Gelato is best stored slightly firmer than soft-serve but softer than typical ice cream.
Serve: Serve slightly warmer than ice cream to release the coffee aroma — scoop into chilled bowls, garnish as desired, or use in an affogato (hot espresso poured over a scoop).