In a large bowl, mix the kumquats with the kosher salt. Let them rest for 2 to 3 hours, or overnight in the fridge, if possible.
Heat the oil in a deep pan for a few minutes on medium heat.
Add the fennel seeds. When they sizzle and darken slightly, after about 2 to 3 minutes, add the curry leaves, ginger, and chilis, frying and stirring for just a minute or two.
Then add the kaffir lime leaves and kumquats. Stir well.
After 5 minutes add the curry powder and stir again.
After 5 more minutes, stir in the water and sugar.
Reduce the heat to medium-low and cook covered for 10 minutes, stirring intermittently to ensure the chutney does not stick to the bottom of the pan. If this happens, stir in more water, 1/4 cup at a time, but the mixture should remain thick and gooey.
Cook just until the chutney has a chunky jam-like consistency.