Combine the sugar and 1 cup water in a saucepan. Lightly bruise the rosemary sprigs without crushing them, then add them and the split vanilla bean to the pan.

Warm the mixture over medium heat, stirring until the sugar dissolves. Bring it only to a gentle simmer, avoiding a vigorous boil, and cook for about 5 minutes.

Remove the saucepan from the heat and lightly bruise the mint leaves before adding them to the hot syrup. Let the mixture steep for 15 to 20 minutes.

Strain the syrup into a heatproof container, removing the rosemary, mint, and vanilla bean. If using vanilla extract instead of a bean, stir 1 teaspoon into the strained syrup after it has been removed from the heat.

Pour the infused syrup and fresh lemon juice into a large pitcher. Add 4 cups of cold water and stir thoroughly.

Taste the lemonade and add the remaining 1 cup cold water if it is too sweet or too strong. Chill for 30 to 60 minutes, then serve over ice with lemon slices and fresh herbs.