Preheat the oven to 350 degrees F (175 degrees C). Grease a 9-inch pan with 2-inch sides and line the bottom with a round of parchment paper.
Add butter pieces to the pan. Place in the preheating oven until melted. Sprinkle brown sugar on top. Arrange sliced pears in a circular pattern over the butter and brown sugar. Set aside.
Whisk graham flour, all-purpose flour, baking powder, baking soda, ginger, salt, and cinnamon together in a medium bowl.
Combine butter, brown sugar, oil, and honey in a stand mixer fitted with the paddle attachment. Beat on medium speed for 2 minutes, scraping the sides of the bowl as necessary. Add eggs and vanilla extract; beat for 1 minute. Add flour mixture in 3 additions, alternating with milk; beat briefly after each addition.
Pour batter carefully over the pears. Smooth the top.
Bake in the preheated oven until golden brown and a toothpick inserted into the center comes out clean, about 25 minutes. Cool cake for 10 minutes. Invert onto a wire rack and peel off parchment paper. Allow to cool completely.