Preheat oven to 350 F. with rack in centre of oven. Prepare a 10-inch springform pan by spraying with baking spray and lining the bottom ring with parchment paper. Place on a baking sheet and set aside.
Prepare the pears: You can peel the pears if you like, or simply leave the peel on. Cut in half down from the stem end to the bottom. Scoop out the core with a spoon and remove the stem spine and bottom blossom end. Place cut side down on a cutting board and cut each half in to 1/4-inch-ish slices. Transfer the sliced halves to the prepared baking pan, cut side down, fanning out the slices slightly. Arrange the sliced halves in a ring around the outside of the pan. The sliced halves should just touch each other in the centre and fan out slightly towards the outside edges. The centre couple of inches should be empty. You may or may not need all your pears. Simply fill until it's filled around. Set aside.
In a large bowl with an electric beater or in the bowl of a stand mixer, beat together the butter and the 1 cup of sugar until pale and fluffy, about 5 minutes.
Add the eggs, one at a time and beat well after each addition, scraping down the sides of the bowl as needed. Beat in the vanilla.
In a medium bowl, whisk together the flour, baking powder and salt. Gradually add the flour mixture to the butter mixture alternately with the sour cream, beginning and ending with flour mixture, beating just until combined after each addition.
Spoon the batter in to the centre of the prepared pan. Using a knife, gently spread the batter in to a thin layer out to the outside edges of the pan. It will seem very thin and barely cover the pears. Scatter the flaked almonds over the centre area of the batter. Sprinkle top of batter evenly with the 1/4 cup white sugar.
Bake in preheated oven until a tester inserted in the centre comes out clean, about 35-40 minutes.
Let the cake cool 5-10 minutes in the pan, then run a knife around the outside and remove the outer ring. Allow to cool a bit more, then slice and enjoy warm with a dollop of Crème Fraîche.
Be sure to read the "Cook's Notes" in the original post, for more tips, options, substitutions and variations for this recipe!