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1
Adjust oven rack to middle position and preheat oven to 350u00b0F. Coat 9-inch round springform pan with cooking spray. In medium bowl, whisk together flour, baking powder, baking soda, and salt; set aside. Pulse sugar, rosemary, and orange zest in food processor until no zest strands remain and rosemary is coarsely chopped (see note).
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2
In large bowl, beat butter, oil, and rosemary-lemon sugar on medium speed until light, about 3 minutes. Add eggs, one at a time, beating well after each addition. Add honey and beat just until incorporated.
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3
Decrease mixer speed to low and add flour mixture in three batches, alternating with milk. Scrape sides and bottom of bowl with rubber spatula as needed. Increase speed to medium and beat mixture just until combined, 20 to 30 seconds. Add vanilla and beat once more, just to combine, about 10 seconds.
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4
Scrape batter into prepared pan. Bake until cake tester inserted in cake comes out clean, 40 to 45 minutes, rotating cake halfway through baking. Transfer cake to cooling rack set inside baking sheet and cool in pan 10 minutes.
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5
Release springform and invert cake onto cooling rack; remove bottom of springform. Invert cake once again and cool completely, about 1 hour.
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6
Melt butter in large skillet over medium heat and cook until beginning to brown, 3 to 5 minutes. Add figs and season with salt and pepper. Cook until figs soften, about 3 minutes. Stir in honey and remove from heat.
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7
With a serrated knife, slice about 1/8 inch off top of cake. Spoon figs and any released juices on top of cake. Serve.
