Lightly butter a 9-inch cheesecake pan with removable rim at least 2 1/2 inches tall. Line pan with a 10-inch round of cooking parchment, pressing into bottom and about 1/2 inch up sides. Cut 2 tablespoons butter into about 1/4-inch chunks and drop evenly over parchment in pan bottom. Sprinkle evenly with 1/2 cup brown sugar and the crystallized ginger.
Peel pears and cut in half lengthwise, then, slicing parallel to cut edge, cut into 1/2-inch-thick slices. With a small knife, cut core from each slice. Arrange slices flat, in a single layer, over sugar mixture in pan, trimming pieces as needed to fit.
In a small bowl, whisk together flour, baking powder, baking soda, ginger, cinnamon, salt, and allspice.
In another bowl, with an electric mixer on medium-high speed, beat remaining 1/2 cup butter and 1 cup brown sugar until well blended. Add eggs, one at a time, beating well after each addition. Reduce speed to medium-low and beat in molasses. Add flour mixture and buttermilk alternately, beating until incorporated, then beat on high speed just until well blended. Pour batter over pears.
Bake in a 325° regular or 300° convection oven until a toothpick inserted in center (not in fruit) comes out clean, 1 hour and 35 to 40 minutes (cake center may settle slightly). Let cool in pan on a rack about 20 minutes. Remove pan sides. Invert a platter over cake, then, holding the two together, invert again. Carefully remove pan bottom and parchment. Serve warm.