Combine the milk and sugar in a small saucepan. Bring to just a simmer over medium heat. Remove from heat.

Whisk in instant coffee powder until well-combined.

In a medium-sized bowl, combine the milk and coffee mixture with heavy cream. Stir in the vanilla.

Cover the bowl with plastic wrap and refrigerate for at least 4 hours or overnight if possible.

Churn the ice cream according to your ice cream maker's instructions. Serve the ice cream immediately for a soft-serve ice cream or freeze it until the desired consistency.