Place lemons in a pot and cover with cold water by an inch (2.5 cm). Cover and bring to a boil, adjust heat and simmer for 1 hour. Keep covered, turn off heat and allow to cool for about 30 minutes.

Position rack in middle of oven. Preheat oven to 375°F/190°C. Coat the inside of a 9-inch (23 cm) springform pan with nonstick spray; set aside.

Meanwhile, pulverize the almonds in a food processor fitted with a metal blade. I pulse on and off, then let the machine run until you have ground the almonds very fine, but not until they get powdery. They should still have a little texture, but not much. Transfer the ground almonds to a small bowl; carefully wipe out the food processor with a paper towel and reassemble with metal blade.

Remove the lemons from their poaching liquid (which can be discarded) and transfer to a cutting board. Slice them into quarters and pick out any seeds (see Tips). Place lemons, and any juice that has exuded from the lemons, into re-assembled food processor and pulse on and off, then process until a thick paste/purée forms; set aside.

Beat eggs and sugar together with an electric mixer on high speed until they are thick and a ribbon forms when you drizzle the mixture back on itself. Fold in the ground almonds and baking powder until almost completely blended, then add puréed lemons and fold in until you get a well-blended batter. Scrape batter into prepared pan.

Bake for 20 minutes, cover top with foil, turn oven down to 350°F/180°C and continue baking for about 40 minutes more or until a toothpick tests clean when inserted in the center. Cool pan on rack or about 20 minutes, then run an icing spatula between cake and pan, then release springform and remove outer ring. Allow cake to cool completely. Cake can be served the day it is made but we think it truly improves after a day or two. Wrap cooled cake in plastic wrap and store at room temperature until needed. Serve cake as is, or with a dusting of confectioners’ sugar or a few berries on the side.