The cocktail made with bourbon, mint, sugar, and crushed ice is a mint julep.
A traditional mint julep combines bourbon with fresh mint, sugar or simple syrup, and crushed or shaved ice. The mint is often gently muddled or pressed so its aromatic oils flavor the drink without turning the leaves excessively bitter. Spearmint is the customary choice, particularly in Kentucky.
The drink has deep roots in the American South. Early descriptions of juleps used different spirits, including rum, brandy, gin, or whiskey, but bourbon eventually became the defining base. The cocktail is especially associated with the Kentucky Derby, where Churchill Downs began promoting it in 1938.
A mint julep is sometimes confused with a mojito because both use mint and crushed ice. A mojito, however, is typically made with rum, lime, mint, sugar, and soda water. A Sazerac and a Manhattan are whiskey cocktails, but neither has the mint-and-crushed-ice profile that defines a julep.