Preheat oven to 350 degrees F. Turn the base of a 9-inch springform pan upside down so you can easily slide the cake off. Line the bottom with a round piece of parchment paper, then lightly spray the pan with vegetable cooking spray.
Peel, core and chop 2 pears. Toss with ¼ cup of flour and set aside.
In a large mixing bowl, whisk together 2 cups of flour, salt, baking powder, baking soda and granulated sugar. Make a well in the center and set aside.
In a small mixing bowl lightly whisk the eggs. Add the sour cream, melted cooled butter, vanilla and almond extracts. Fold together with a rubber spatula until blended. Set aside.
Pour the sour cream mixture into the flour mixture and fold together with a spatula until most of the flour is incorporated. The batter will be thick and seem a little dry. Immediately add the pears, and any pear juice, and half the chopped ginger. Fold together until incorporated. Scoop the batter into the prepared pan and smooth the top. Sprinkle the remaining chopped ginger over the top of the cake.
Set aside to rest for 10 minutes before baking. While the cake is resting, slice the remaining peeled and cored pear into 8 to 12 slices. Top the unbaked cake with the pear slices and lightly press into the batter. Sprinkle with 1 tablespoon of coarse or granulated sugar.
Bake at 350 degrees F until a toothpick comes out with no wet batter, about 65-75 minutes. Tent with foil during baking if needed to prevent over-browning.
Allow the cake to cool on a rack for 30 minutes before removing the sides of the pan. Slide onto a serving plate, cut into wedges and enjoy slightly warm or cooled. Dust with powdered sugar and serve.
Store leftovers in a sealed container at room temperature for a day or two, or refrigerate for longer storage.