Muddle 3 fresh mint leaves with 1/2 a cup of sugar until the mint is just crushed slightly and releases its flavor. Add to a small sauce pan with 1/2 cup of water. Cook over low heat until the sugar dissolves, stirring constantly. When sugar dissolves, remove from the heat and pour into a strainer over a jar. Let cool.
For the drinks, add all the ingredients to a shaker with ice. Shake until the shaker is frosty, about 10 seconds. Pour into sugar rimmed glasses and garnish with fresh rosemary sprigs and mint leaves.
Notes
Feel free to adjust the amount of simple syrup to suit your desired sweetness level. If you want it sweeter use a bit more, if you want it less sweet use less.You can also make the mint simple syrup more minty by adding more mint leaves.