Make the cranberry simple syrup:
In a small saucepan combine cranberries, water, sugar, and vanilla extract. Bring to a boil over medium/high heat. Reduce the heat to low and simmer until the sugar dissolves and the cranberries burst and wrinkle.
Remove from heat and allow to come to room temperature. Strain into a container with a tight fitting lid, pressing on the solids to extract as much liquid as possible from the cranberries. Discard the solids or save for another use (like spooning it in your mouth with abandon!). Seal and place in the refrigerator until ready to use.
Make 1 Cranberry Tangerine Mojito:
To an 8 ounce (or any tall) glass, add the mint leaves and cranberry simple syrup. Muddle with a muddler or back of a wooden spoon until the mint is slightly crushed and fragrant. Add the tangerine slices and muddle until the tangerines have released their fragrance and juice. Add rum, followed by the ice. Finally add the seltzer. Give it quick stir to incorporate the ingredients and sip. Mojitos are sipped.
Simple syrup is enough for several mojitos.