Preheat the oven to 400 degrees F. Line an 8×8 baking pan with parchment paper.
In a medium bowl, combine the flour, butter, sugar, lemon zest, salt, egg yolk, and vanilla extract with your fingertips, rubbing it all together until it forms a crumbly pile of ingredients. Dump this mixture into the lined baking pan and press it into the pan well until you have a flat crust. Bake for 20-25 minutes until the crust is golden brown.
With a hand mixer or a stand mixer (with the paddle attachment), beat together the cream cheese, sugar, sour cream, and vanilla until smooth and combined. Add the eggs and egg yolks one at a time, waiting until each egg is incorporated into the filling before adding the next. Mix in the flour.
Pour the cheesecake filling over the parbaked crust, then place the pan into a larger pan (I used a 9×13). Fill the larger pan with enough boiling water to come halfway up the sides of the 8×8 pan. Place the cheesecake in the oven, turn the heat down to 350, and bake for 30-35 minutes, until the cheesecake has set. You can test for this by jiggling the pan a little bit. The cheesecake should be slightly jiggly, but no liquid cheesecake should be swirling around.
Remove the cheesecake from the oven but leave the cheesecake in the water bath until it has cooled, then chill the cheesecake for at least 4 hours.
To prepare the raspberries, place the raspberries in a saucepan with the lemon juice and sugar, and cook for 5 minutes over medium high heat, until softened. Pour the caramel over the cheesecake, then spoon some cooked raspberries on top as well. Enjoy!