In a small, dry skillet over medium heat, toast mustard seeds and anise seed. Gently shake the pan back and forth until seeds are aromatic and lightly toasted, about 1-2 minutes.
Transfer seeds to a heavy, small saucepan with remaining ingredients. Bring to a boil stirring often.
Reduce heat to medium-low and simmer until the chutney thickens and the kumquats become translucent, about 20-25 minutes.
Transfer to a bowl and let cool before serving.
Store in air-tight container in the refrigerator for up to two weeks. Bring to room temperature before serving.
Notes
Recipe adapted from the Kumquat Growers Association