Place the sugar, water, and peppercorns in a small saucepan.

Bring to a boil for one minute, then turn off the heat and let cool (you can move to the fridge when it's cool enough). This step can be done in advance.

While the syrup is cooling, thinly slice the kumquats, flicking/squeezing out the seeds (they're fairly edible, so no worries if you don't get them all, but in general people don't like seeds in their beverages).

Place the sliced kumquats in a large pitcher (or divide between three quart jars).

Pour a little of the cooled syrup over them, and muddle with a muddler (or the handle of a wooden spoon) to smush the kumquat slices and release their oils and juices.