Fill a glass coffee mug with boiling water. Let stand 30 seconds. Dump water and dry outside of mug.
Place rum, kumquat syrup, lime juice and bitters in mug. Pour in boiling water. Garnish with kumquat slices.
CANDIED KUMQUATS & SYRUP
Slice kumquats into ¼-inch-thick (5-mm) rounds. Using a skewer, poke out seeds.
In a small saucepan, bring water and sugar to a boil over medium-high heat, whisking to dissolve sugar. Add kumquat slices. Reduce heat to maintain gentle simmer. Cook, stirring occasionally, until kumquats are tender, about 12 minutes. Remove from heat and cool completely.
Transfer kumquats and their syrup to a glass jar with lid. Refrigerate up to 1 month.