Place water, sugar and honey in a saucepan over medium-low heat.

Meanwhile, juice lemon and set aside the juice. Cut leftover lemon into quarters and add to saucepan (with sugar mixture).

Bring to a boil, stirring occasionally. Add rosemary. Turn down temperature to low and simmer until mixture becomes syrupy (about 10 minutes), stirring occasionally. Remove from heat and allow to cool.

Juice Grapefruits. Add lemon juice to the grapefruit juice and pour entire mixture through a sieve.

Once syrup is cool, pour through a sieve into juice mixture. Stir to combine.

Add 1-2 ounces of vodka or white rum to bottle (10-12 ounce size). Pour in 5-6 ounces of juice mixture. Top with soda or sparkling water. Seal. Chill before serving.

Add ice cubes to glass along with 1-2 ounces of vodka or white rum. Pour in 5-6 ounces of juice mixture. Top with soda or sparkling water. Garnish with grapefruit segment and tiny sprig of rosemary.