Quarter kumquats lengthwise; cut off the white center membrane and remove seeds.

Slice quarters into small pieces.

Place kumquats into a pot. Add sugar, water, lemon zest (white part only), lemon juice, star anise, and a pinch of cayenne; mix together. Cover and let sit at room temperature for 2 or 3 hours to allow fruit to macerate. Or you can refrigerate overnight.

Place the pot over medium-high heat and bring mixture to a simmer, stirring occasionally. Reduce heat to medium; cook and stir occasionally for 10 minutes.

Continue cooking and stirring often until mixture is thick enough so that if you scrape a spatula across the bottom of the pan, you can briefly see the bottom of the pan before marmalade spreads back out, 30 to 40 minutes. Mixture should reach a temperature of 215 to 220 degrees F (100 to 105 degrees C).

Remove from heat and allow to cool slightly, 5 to 10 minutes.