Prepare the Topping: Cook butter in a 10-inch cast-iron skillet over medium until butter is lightly browned and has a nutty and toasted aroma, about 5 minutes. Remove from heat. Immediately add brown sugar, ginger, cardamom, and cinnamon, and stir until smooth.

Peel, halve, and core pears. Cut the halves from top to bottom into 1⁄4-inch-thick slices, and press gently to fan the slices. Carefully -place pears on Topping in skillet. (Don’t pack them in—you might have a few left over.) Set skillet aside.

Prepare the Cake: Preheat oven to 350°F. Whisk together flour, baking powder, ginger, cinnamon, cardamom, allspice, cloves, and salt in a medium bowl.

Beat butter and brown sugar in a large bowl with mixer on high speed until light and fluffy, about 2 minutes, stopping to scrape down sides of bowl. Add eggs, 1 at a time, beating well after each addition.

Add half of flour mixture to butter mixture; beat on medium speed until smooth, about 2 minutes. Add milk, molasses, and vanilla, and beat until smooth, about 3 minutes. Add remaining flour mixture; beat 2 minutes, stopping twice to scrape down sides of bowl. Pour batter over Topping and pears in skillet, and gently spread to edges.

Bake in preheated oven until Cake is golden brown and springs back when touched lightly in center, 30 to 40 minutes. Cool in skillet on a wire rack 5 minutes.

Carefully invert warm Cake onto a serving platter. (Some pear slices might stick to the skillet; gently loosen and replace on cake.) Cool completely, about 45 minutes.