Position the racks in the top and bottom thirds of the oven; preheat to 200°. In the bowl of a stand mixer, beat the bean liquid until firm peaks form, about 5 minutes; beat in the vanilla. With the mixer running, gradually add 1 cup sugar; continue beating until very stiff peaks form and the mixture resembles shaving cream, 5 to 10 minutes more (timing will vary from can to can). Line two baking sheets with parchment. Scoop 4 rounded 1/2 cups of the whipped bean liquid onto each sheet, spacing evenly apart. Using the back of a spoon, create a well in the centers, keeping the rounds about 4 inches in diameter. Bake, rotating the sheets halfway through, until firm, about 2 1/2 hours (the meringues may spread slightly). Turn off the oven and let the meringues cool in the oven 2 hours. Transfer, on the parchment, to wire racks; let cool completely. Peel the meringues off the parchment. (The cooled meringues can be stored airtight up to 1 day.)
Meanwhile, in a medium saucepan, add the remaining 2 cups sugar, cinnamon sticks, ginger and 1 cup water. Using a vegetable peeler, remove the zest (green part only) from 1 lime and add to the pan. Bring to a boil over high, stirring often to dissolve the sugar. Reduce the heat to medium-low; add the kumquats. Let simmer until the kumquats are tender, deep orange and translucent, about 15 minutes. Transfer to a bowl. Juice the zested lime (about 2 tbsp.) and stir into the candied kumquats; let cool.
Discard the cinnamon sticks, ginger and lime zest from the kumquats. Pour the cream into a large bowl. Grate the zest from the second lime into the cream. Using an electric mixer, beat until firm peaks form. To assemble the pavlovas, fill the meringues with whipped cream. Using a slotted spoon, top with the kumquats. Sprinkle with the nuts.