Add the cream cheese to the bowl of a stand mixer fitted with the whisk attachment (or a large bowl and electric hand mixer) and whip on medium speed until it's smooth and creamy. Scrape down the bottom and sides of the bowl as needed.
Add the creamy peanut butter, sour cream, granulated sugar, and all-purpose flour to the cream cheese and beat until fully combined. Scrape the bottom and sides of the bowl as needed.
Add the room-temperature eggs and yolk, one at a time, and beat until just combined, scraping down the bowl between each addition. Do not overmix the batter.
Pour the batter into the prepared springform pan. Tap the pan against the counter a few times to release any air bubbles in the batter.
Place the springform pan into a larger roasting pan, then open the oven and place it on the center rack. Carefully pour boiling water into the roasting pan until the water is about halfway up the sides of the pan, then close the oven.
Bake for 55-65 minutes at 325 degrees, or until the top looks slightly dry and while the middle is still a little wobbly. Be careful not to overbake the cheesecake.
Turn the oven off and open the door about an inch. You can use a dishtowel stuck in the opening to keep it propped open.
Leave the cheesecake in the oven for 30-45 minutes or until the oven is just slightly warm. This will help prevent cracks from forming.
Remove the pan from the oven and remove the springform pan from the water bath.
Run a dinner knife around the edge of the cheesecake in case it's sticking to the pan. Place the pan on a cooling rack to let the cheesecake cool completely.
Once cooled, refrigerate in the pan for at least 6 hours (overnight is best) to let it set and chill completely.