Preheat the broiler on low. Line a baking sheet with a silicone baking mat.
Sprinkle 2 teaspoons of the turbinado sugar in a 3 1/2-inch circle on the baking mat; you can use a biscuit cutter as a template if needed. Repeat with the remaining sugar to make 4 sugar circles/discs. Broil until the sugar melts and caramelizes, 1 to 2 minutes. Let cool completely.
To each of 4 coffee mugs add: 1/4 cup rum cream liqueur, 1 tablespoon light cream, 1 teaspoon vanilla extract and 1 cup coffee. Carefully remove the caramelized sugar discs from the baking mat and place 1 disc on top of each mug. Crack the sugar with a spoon, let it fall into the coffee and stir to dissolve.