In the bowl of a stand mixer fitted with the paddle attachment, add the butter, peanut butter, and sugar, then beat at medium speed until creamy and lightened in color, about 4 minutes. Stop every minute or so to scrape down the sides and bottom especially, as the peanut butter likes to stay separated.
Add the eggs one at a time, beating well (about 30-60 seconds at least) on medium speed after each addition. Beat in the sour cream and the vanilla extract, and scrape down the sides of the bowl again.
In a separate bowl, whisk together the flour, baking powder, and salt. Measure out the whole milk and place it in a container with a spout (ideally) so it can be easily poured. You will add the flour and milk in three parts, starting with the flour.
Running the mixer at the lowest speed, slowly add ⅓ of the flour mixture, beating until just barely incorporated, then pour in ½ the milk, beating until just barely incorporated. Repeat this process for the second ⅓ of the flour, the other ½ of the milk, then the final ⅓ of the flour.
Once everything has been just barely incorporated, pour about half the batter (470 grams) into the prepared cake pan. Spoon the warmed chocolate-hazelnut spread over the batter, then gently spread it out to cover the batter out to the edges of the pan. Cover the chocolate-hazelnut layer with the second half of the coffee cake batter, then smooth out the top with an offset spatula. Evenly sprinkle the top with the prepared peanut butter crumble.
Baked the coffee cake for about 50 minutes. If necessary, cover the top of the coffee cake midway through baking if the crumb is browning too quickly. The cake is done when a tester inserted in the center comes out clean, with no crumbs stuck to it. Be careful here, as my final tester looked clean but my cake was slightly underdone.
Let the cake cool 10 minutes in the pan, then remove the sides and bottom of the springform pan and let the cake continue cooling on a wire rack.
Serve this coffee cake warm or at room temperature, with a side of fresh berries and whipped cream if desired.