In a medium saucepan, combine whole milk, heavy cream, sugar, and a pinch of salt. Warm gently over medium heat until sugar dissolves, avoiding boiling.

In a separate bowl, combine strong brewed coffee with instant espresso powder until fully dissolved.

Slowly pour the coffee mixture into the milk and cream mixture while stirring continuously.

Whisk the egg yolks in a bowl until smooth and pale.

Temper the egg yolks by gradually pouring in a cup of the warm milk mixture while whisking vigorously.

Combine the tempered egg mixture back into the saucepan, stirring constantly.

Cook the mixture over medium-low heat, stirring frequently, until it thickens and coats the back of a spoon, about 8-10 minutes.

Strain the mixture through a fine-mesh sieve into a clean bowl.

Stir in vanilla extract and let cool to room temperature. Cover and refrigerate for at least 4 hours, preferably overnight.

Pour the cold custard into an ice cream maker and churn according to manufacturer's instructions, about 20-25 minutes.

Transfer the churned gelato into an airtight container, smooth the top, and freeze for at least 4 hours before serving.