Wash and trim 2 lemons and then boil in a saucepan with enough water to cover until very soft and deflated, 1 hour. Discard the liquid and break open the lemons to remove the seeds. Pulse the whole lemons in a food processor until chunky like marmalade. Add 2 Tbsp orange zest, 2 tsp vanilla extract, and 2 Tbsp honey and pulse until combined.
Preheat the oven to 350℉. Line a 9-inch cake pan or springform pan with a piece of wet crumpled-up parchment paper. This helps line the pan and prevents the cake from burning.
In a stand mixer with the whisk attachment, whip 5 egg whites on high with a pinch of salt until stiff. Transfer to a clean bowl and set aside. In the same stand mixing bowl, beat 5 egg yolks and 1 cup [200 g] sugar on high speed until pale and thick, about 3 minutes. Fold in 3 cups [300 g] almond flour and 1 tsp baking powder using a rubber spatula. Add the lemon puree and continue to fold until completely combined.
Fold ⅓ of the whipped egg whites into the almond mixture using a rubber spatula to loosen the batter. Add the remaining egg whites and gently fold scraping the bottom and sides until fully incorporated. Pour the batter into the prepared pan and sprinkle with ¼ cup [30 g] sliced almonds.
Bake until a toothpick inserted into the center comes out clean, about 50 to 60 minutes. Watch the cake in the last 10 minutes as it can brown quickly. Cover the top with foil if it begins to burn. Allow the cake to cool fully in the pan before unmolding.
While the cake cools, make the macerated blackberries. Add 12 oz [340 g] blackberries to a medium-sized bowl with 2 Tbsp sugar and 2 Tbsp limoncello and then toss to coat. Set aside until ready to serve the cake. Just before serving, fold in 1 to 2 sprigs of finely chopped basil leaves.
Dust lightly with confectioner's sugar and serve with the macerated blackberries. The cake will keep in an airtight container at room temperature for up to 1 week.