Make simple syrup (if needed): Combine equal parts sugar and water in a small saucepan. Heat until sugar dissolves completely. Cool before using.
Muddle the mint: Place mint leaves in the bottom of your julep cup. Gently muddle to release the oils, but don't tear the leaves.
Add raspberries and muddle again lightly to release their juice.
Pour in bourbon and simple syrup, then fill halfway with crushed ice.
Stir for about 15 seconds to chill the mixture.
Add more crushed ice to form a dome on top of the drink.
Garnish with a mint sprig and fresh raspberries. Dust with powdered sugar if desired.
Serve immediately with a short straw.