Preheat oven to 350. Grease bottom and sides of a 2-inch cake pan with 2-inch sides with 1 teaspoon butter. Line bottom of pan with parchment paper; grease top of parchment paper with 1/2 teaspoon butter.
In a small saucepan, melt 1/2 cup butter over medium-low heat. Stir in brown sugar and honey, and cook, stirring frequently, for 4 minutes or until sugar dissolves and mixture is smooth. Let cool slightly; pour sauce into prepared pan. Arrange fig halves, cut sides down, in concentric center over sauce.
In a large bowl, beat remaining 1 cup butter at medium speed with a mixer for 1 to 2 minutes or until creamy. Add sugar and vanilla and beat for 3 to 4 minutes or until creamy. Add eggs, one at a time, beating well after each addition.
In a medium bowl, combine flour, baking powder, salt and cinnamon; gradually add to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition. Spoon batter over figs in prepared pan.
Bake for 45 to 50 minutes or until a wooden pick inserted in center of cake comes out clean. Cool in pan on a wire rack for 1 hour. Carefully run a knife around edge of cake to loosed, and invert onto a serving plate.