For the cakes:
1/3 cup extra-virgin olive oil, plus more for the pan
1/2 cup all-purpose flour, plus more for dusting
1/4 cup cocoa powder
1/4 teaspoon salt
1/3 teaspoon baking soda
1/2 cup sugar
1 large egg plus 1 egg yolk
1/2 teaspoon vanilla extract
1/2 teaspoon finely grated lemon zest
6 fresh figs, halved
4 ounces bittersweet chocolate, chopped
2 teaspoons honey, plus more for drizzling
2 teaspoons extra-virgin olive oil
Large pinch of salt
1/2 teaspoon coarsely ground black pepper, plus more for topping
Combine the sugar, egg and egg yolk, vanilla and lemon zest in a stand mixer fitted with the whisk attachment and beat on medium-high speed until pale and thick, about 1 minute. With the mixer running, drizzle in the olive oil. Add the cocoa mixture and beat until combined. Reduce the mixer speed to low, add the flour mixture and beat until just incorporated.
Divide the batter evenly among the prepared muffin cups. Bake 10 minutes, then top each cake with a fig half and continue baking until a toothpick inserted into the center comes out with a few crumbs, 8 to 10 more minutes. Let cool in the pan on a rack, 20 minutes. Remove the cakes from the pan and let cool completely on the rack.
Make the glaze: Put the chocolate, honey, olive oil, salt and pepper in a microwave-safe bowl and microwave in 30-second intervals, stirring, until smooth.
Top the cakes with the glaze, a drizzle of honey and more pepper. Quarter the remaining 6 fig halves and arrange on top.