In a medium saucepan over medium heat, combine whole milk, heavy cream, sugar, and salt. Stir until the sugar dissolves and mixture is warm, about 5 minutes.

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

Gradually pour the coffee mixture into the warm milk and cream, stirring continuously until combined.

Whisk the egg yolks in a separate bowl until smooth and pale, about 2 minutes.

Gradually mix in about one cup of the hot coffee mixture to the yolks while whisking to temper them.

Return the tempered yolk mixture to the saucepan with the remaining coffee base and cook on medium-low heat, stirring constantly for 8-10 minutes.

Pour the custard through a fine-mesh sieve into a clean bowl to remove curdled bits.

Stir in the vanilla extract into the strained mixture while it's still warm, then let it cool to room temperature, about 30 minutes.

Cover the bowl with plastic wrap and refrigerate for at least 4 hours, or overnight, until completely chilled.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions for 20-30 minutes.

Transfer churned gelato into an airtight container and freeze for at least 4 hours to firm up.

Scoop into bowls and serve with freshly brewed espresso or drizzled with chocolate sauce.