For the nicest possible green color in the finished cake, blanching the pistachios, or removing their inner dark-colored seed coat, is a necessary step. Bring a small pot of water to a boil and add a handful of nuts at a time. Once water returns to a boil, remove nuts with a slotted spoon and rub off seed coat. Dry nuts on a towel, then transfer to a baking sheet and toast in a 300°F oven for about 10 minutes; don't let them brown. Prepare nuts for both the cake (1 1/2 cups) and the topping (1 cup) at the same time.

Butter a 9-inch springform pan; line bottom with a circle of parchment; butter the parchment and dredge with flour, tapping the pan to shake out excess.

Heat the oven to 325°F.

Using a food processor, grind 1 1/2 cups of prepared nuts with flour to a fine meal. In a small bowl, beat egg yolks with half of the sugar until thick and lightened in color. In a large bowl, beat egg whites with salt and cream of tartar into stiff peaks; slowly beat in remaining sugar until they hold stiff peaks again. Drizzle egg yolk mixture into the bowl with egg whites; grate orange rind over yolk mixture; and drizzle in the orange flower water. Sprinkle in 1/4 of pistachio-flour mixture and partially fold everything together. Add another 1/4 of nut mixture and partially fold in; continue until all the nuts are used and the batter is just uniform. Gently scrape batter into prepared pan. Bake for 35–40 minutes, or until cake is set and a toothpick inserted in the center comes out clean. Cool in pan for 10 minutes, then remove pan and cool completely on a rack.

For topping, chop 1 cup of nuts carefully into about 1/8-inch chunks. Stir orange flower water and salt into the warm jam and paint the top and sides of the cooled cake. Pat chopped pistachios into the jam in an even layer.

For the citrus compote, finely grate the zest of one orange into a bowl. Using a small, sharp knife, peel the oranges and release the sections from their membranes into the bowl with the zest, squeezing all juice from the membranes. Trim stem ends of kumquats, and slice thinly, discarding seeds as you go. Stir kumquats and a very few drops of orange flower water into the oranges.

Serve slices of cake with a spoonful of the citrus compote on the side and a dollop of softly whipped cream on top.