In a large mixing bowl (preferably one with a spout), combine the gelatin with 1-2 tablespoons of water, enough to dissolve the powder. Let stand for 5 minutes.
Meanwhile, heat the milk, sugar and vanilla in medium-sized saucepan set over medium-high heat. Whisk to help the sugar dissolve. Once the mixture is simmering, remove from the heat and pour over the gelatin. Whisk until the gelatin and milk are combined, gently scraping the bottom of the bowl to make none of the gelatin is left behind. (Note: If the milk foams up slightly, use a spoon to discard the foam before proceeding with the next step).
Divide the mixture evenly between 6 serving cups (wine glasses or small mason jars are a great option). Place in the refrigerator until firm, at least 3 hours.
Prepare the Coffee Syrup:
Add the sugar and water to a small saucepan and turn the heat to medium high. Once the mixture is simmering, stir several times to help the sugar dissolve. You can either remove it from the heat as soon as the sugar dissolves, or let the syrup reduce for several minutes to a thicker consistency.
Remove from the heat and stir in the vanilla extract. Allow to cool for at least 5 minutes, then stir in the coffee or espresso. Chill alongside the panna cotta.
To serve, top each panna cotta with 1/4 cup or more of the coffee syrup.