Add fresh mint leaves and sugar to a mixing glass. Use a muddler or fork to muddle the sugar and mint together to form a thick paste. Add bourbon and fill mixing cup with normal ice (not crushed) to chill. Stir to mix bourbon and sugar together well.
In a julep glass (or any cocktail glass honestly), fill with crushed ice until overflowing. Strain bourbon into the crushed ice. Garnish with fresh mint and serve with a straw.
Optionally, add a splash of club soda to lighten up the cocktail a bit, although it will also dilute as the ice melts.