Set the oven and prepare the syrup. Preheat the oven to 350°F. Mix 1½ teaspoons of the espresso powder into the syrup.
Line the bottom of the pan with figs and syrup. Drizzle 2 tablespoons of the espresso-syrup evenly over the bottom or the prepared cake pan. Set aside. Cut the figs into thin (about ¼ inch) slices and place them, in one even layer, on top of the syrup in the pan. Set aside.
Make the batter. Add the softened butter and the sugar to a large mixing bowl. Mix until it's completely smooth. Then add ¼ cup of the espresso-syrup, vanilla and sour cream. Once you have a smooth consistency again, blend in the eggs, one at a time. Then add the flour, baking powder, baking soda, cinnamon and salt. Stir just until it's mixed in and smooth.
Assemble. Spoon about half of the batter on top of the fig slices and gently even it out with the bottom of a spoon or offset spatula. Add the filling evenly on top and evenly spread that as well. Then drizzle it with the remaining ¼ cup of espresso-syrup. Spoon the rest of the batter in the pan and smooth it out.
Bake. Place the cake pan on a baking sheet and bake in the preheated 350°F oven until the top is golden brown and is slightly cracked, about 1 hour. It should rise all the way to the top, if not a tiny bit above it.
Cool, invert and serve. Let the cake cool in the pan for about 10 minutes. Then use a knife to very carefully go around the edges (only if it seems like it's sticking anywhere). Now place a large serving platter or plate upside down, on top of the cake pan and invert it. Gently remove the parchment paper from the top of the cake. Let it cool for at least an hour before serving.