Oh, before I get into too many details, I should mention that this odd little paste is simply chock-full of amazingly crazy flavor. The Lees suggest stirring a spoonful into a Bloody Mary, and that is a very good idea, indeed. I tried it myself and was pleased as punch. I wasn't really willing to stop there, though. With a bit of experimenting, I found it works nicely smeared on a crostini or cracker (add a bit of creamy chevre or feta for even more deliciousness), served alongside a nice roasted chicken, or simply snacked on with a spoon when no one is looking.
To make the paste: Preheat an oven to 300°F. Cut 8 oz. of kumquats in half crosswise and use your thumbnail to work out the flesh and pith. Put the rinds on a parchment paper- or foil-lined baking sheet and the flesh and pith in a small bowl. Remove the stems and seeds from 4 large jalapeño chiles, cut the chiles into large pieces and put them on the baking sheet, too. Bake the kumquats and chiles until the rinds are relatively dry and the chiles are wilted and very well wrinkled, about 30 minutes. Turn off the oven and let everything sit in there and dry out some more. Let everything cool and then whirl the kumquat rinds, chiles, and about 1/2 tsp. fine sea salt in a blender or food processor to make a paste. You'll need to pulse it and scrape down the sides a few times to make a real paste - don't go so far as to whirl it into a full-on purée, though, since you want to have a bit of the chewy texture from the dried kumquat peels in there. Taste and add more salt to taste, if it needs it. Remember the kumquat fruit you kept in a small bowl? Squeeze out some juice from that and add a teaspoon or two to the paste. Taste the paste and add more kumquat juice and/or salt to make the flavor pop as much as possible.
Transfer the paste to a small jar and store in the fridge. Always use a clean spoon to take and paste out - this will help minimize the chances of bacteria or mold making its way into the paste and help make it last longer. If you don't go through it in a shot (we did with the first round at my house, that's for sure!), it will keep for several weeks if kept properly uncontaminated and chilled.