For the cake: Preheat the oven to 350 degrees F. Grease the bottom and sides of two 9-inch round cake pans with 2 tablespoons of the butter.
Make the cake batter: In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and granulated sugar on medium speed until smooth, 5 to 8 minutes. Add the eggs, one by one, and then add the lemon zest and juice. In a medium bowl, sift together the flour, baking powder and salt. Remove the bowl from the machine and stir in the dry ingredients. Do not overmix.
Bake the cake: Fill each prepared cake pan with half of the batter. Place the pans in the center of the oven and bake until a toothpick inserted in the center of each cake emerges clean, 30 to 35 minutes. Cool the cakes in the pans on wire racks until cool enough to handle, then turn the cakes out onto the racks to cool completely.
For the filling: In a medium bowl, whisk the ricotta until smooth. Sift in the confectioners' sugar, cinnamon and nutmeg. Mix to blend. In a separate bowl (or in the bowl of an electric mixer fitted with the whisk attachment), beat the heavy cream until fairly stiff.
Using a rubber spatula, gently fold the cream into the ricotta mixture. Stir in the chocolate chips and lemon zest.
For the rum glaze: Bring the rum to a simmer in a medium pot over low heat. Sift in the confectioners' sugar and a pinch of salt and simmer, whisking, until smooth, 2 to 3 minutes. Cool.
Assemble the cake: Place one layer of the cake on a flat surface. Brush some of the rum glaze on the first layer and top with all of the ricotta filling. Place the second cake squarely on top and gently press the two layers together. Brush the second cake with rum glaze.
For the toppings: Frost the whole exterior of the cake with the whipped cream. Sprinkle on the chocolate chips over top. Serve immediately or refrigerate until serving.