Place the roasted hazelnuts in a food processor and pulse until finely ground to a flour-like consistency. Measure out about 1 cup and set aside.

Preheat the oven to 350°F. Grease a 9-inch round cake pan and line the bottom with parchment paper. Then, grease the sides with butter.

Melt the 4 tablespoons of butter and pour it into the prepared pan. Sprinkle the brown sugar evenly over the butter, then arrange the pear slices in overlapping concentric circles over the sugar mixture. Set aside.

In a medium bowl, whisk together the ground hazelnuts, flour, baking powder, baking soda, and salt.

In a large bowl, beat the butter, granulated sugar, and brown sugar until light and fluffy, about 4 minutes. Beat in the eggs one at a time, then add the vanilla and mix in the sour cream.

Add the dry ingredients in two additions, alternating with the milk, mixing just until combined.

Carefully spread the batter over the arranged pears and smooth the top.

Bake it for 45 to 55 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pan for 15 minutes.

Run a knife around the edge of the pan, place a serving plate on top, and carefully invert. Remove the parchment paper and allow the caramel topping to settle for a few minutes before slicing.