To prepare the simple syrup, combine 1 cup sugar and 1 cup water in a pan. Bring to a boil and stir until sugar dissolves. Remove from heat and allow to cool.
Place two mint leaves in your palm and clap your hands a couple of times to release the oils.
Rub the mint leaves all along the inside of a julep cup.
Place 8 to 10 mint leaves in the bottom of the cup, along with 1 ounce of simple syrup. Use the back of a spoon or a wooden muddler to gently bruise the leaves.
Fill the julep cup halfway with ice and add bourbon.
Stir until the cup is frosty, then fill with ice and stir gently once more.