Heat all ingredients for the strawberry simple syrup (except pure vanilla extract) in a saucepan over medium heat. Cover and bring to a full boil, stirring occasionally. When strawberries begin to soften, mash them with a fork. Reduce heat to a simmer and cook at least 10 minutes. Remove from heat and allow mixture to cool to room temperature. Strain through a fine mesh strainer, discarding the strawberry pulp or save it for a smoothie or muffin recipe. Store simple syrup in an air-tight container in the refrigerator until ready to use.
Fill a shaker with ice and add the ingredients for one Moscow Mule. Shake well and serve in a copper mug filled with ice with a lime wedge and a sprig of fresh mint.