Preheat the oven to 180 degrees. Grease and line a 22cm round springform pan.
Place the butter and sugar in the bowl of an electric mixer and beat on medium speed for 3 minutes, until light and fluffy, scraping down the bowl with a rubber spatula. With the mixer on medium speed, add the eggs, one at a time, scraping down the bowl and mixing until smooth.
Add the ricotta, sour cream, vanilla, and lemon zest and mix until combined.In a small bowl, sift together the flour, baking powder and salt. With the mixer on low, slowly add the dry ingredients to the batter, mixing just until combined. Pour the batter into the prepared pan and smooth over the top with a spatula.
Arrange the figs on the cake, cut side up. Drizzle the honey over the top of the cake and bake for 35 to 45 minutes, until browned and a skewer inserted in the center comes out clean.
Allow the cake to cool before turning out onto a wire rack, place a plate over the bottom of the cake and flip it over so the cake is plated with the figs facing upwards. Serve with greek yogurt or crème fraiche.