For the cupcakes: Preheat the oven to 325 degrees F. Line muffin pans with 24 muffin liners. In a medium bowl, whisk the flour, baking soda, baking powder and salt until well combined. In the bowl of an electric mixer with the paddle attachment, cream the butter, oil and brown sugar.
Add the eggs, one at a time, scraping the bowl as needed.
Add the figs and lemon zest and mix for about a minute until well combined. With the mixer on low, gradually add the flour mixture just until combined. Then remove from the mixer and scrape by hand. Fill the prepared muffin pans three-quarters full with batter and bake until a toothpick inserted comes out clean, about24 minutes.
For the fig compote: In a medium saucepan over medium heat, combine the figs, granulated sugar, 1/4 cup water and the honey. Bring to a boil and stir until the water has evaporated and the figs are soft.
Add the sea salt and refrigerate until cool.
For the frosting: Whip the cream cheese and butter in an electric mixer with the paddle attachment until fully incorporated. With the mixer on low, gradually add the powdered sugar until combined.
Add the vanilla and mix until fully incorporated.
To assemble: Use a knife to make a hole in the center of the cupcakes. Fill with salted honey fig compote, and then frost with cream cheese frosting.
