Homemade Coffee Liqueur

Place the coffee grounds in a 2-cup measuring cup or small pitcher, add 1 3/4 cups of the water, and stir to combine. Cover with plastic wrap and let steep at room temperature for at least 12 hours and up to 1 day.Line a fine-mesh strainer with a standard coffee filter and fit it over a medium bowl. Working in batches, slowly pour the coffee into the filter until all of the liquid has passed through the strainer (the coffee will pass through in a slow stream; don’t force it through); stop when you reach the solids at the bottom of the pitcher—don’t pour them in. Discard the grounds and the contents of the strainer.

Transfer the coffee to a 1-quart container and set it aside.

Place the remaining 1/2 cup of water and sugar in a small saucepan over high heat and bring it to a simmer, stirring to dissolve the sugar.

Remove from the heat and let cool to room temperature, about 30 minutes.

Add the cooled syrup and rum to the container with the coffee. Using a knife, split the vanilla bean in half lengthwise and scrape the seeds out of the bean, add both the seeds and pod to the coffee mixture (make sure the pod is submerged), and stir to combine. Tightly cover the container and let it sit at room temperature in a cool, dark place for at least 2 weeks, shaking once a week.