Preheat the oven to 330°F, with a rack in the middle. Oil a 10- or 11-inch cast-iron skillet.
To make the cake, stir together the flour, ground ginger, salt, cinnamon and allspice in a bowl. Set aside.
In a large bowl, beat butter and both sugars with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in almond extract and fresh ginger.
With mixer on low speed, gradually add flour mixture to butter mixture alternately with yogurt, beginning and ending with flour mixture, beating just until combined after each addition.
Fold in half of pears (this part cut in cubes). Spoon batter into prepared skillet, spreading to edges. Arrange remaining pears on top, slightly pressing into batter. Sprinkle with spiced sugar.
Bake until a wooden pick inserted in center comes out clean, about 50 minutes. Transfer the skillet to the stove top to cool for at least 20 minutes.
Serve warm or at room temperature, cut into wedges. Refrigerate leftover cake, tightly covered, for up to 4 days, or freeze, tightly wrapped, for up to 2 months. Bring to room temperature before serving.