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1. Preheat your oven to 375 F. Liberally grease the bottom of a 9 1/2 inch spring form pan with butter and then prepare the crust.
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2. Combine the graham cracker crumbs, melted butter and brown sugar in a bowl and stir it together until it resembles wet sand. Press it firmly and evenly across the bottom of the prepared spring form pan to form the crust and then bake it in the oven for about 10 minutes, until golden and set. Take it out of the oven, let it cool slightly and reduce the oven temperature to 350 F.
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3. In the meantime, prepare the cheesecake filling. In the bowl of a stand mixer fitted with the paddle attachment, combine the cream cheese, sugar and vanilla and beat it thoroughly until smooth. Add in the eggs and egg yolks one at a time, letting each get beaten in before adding the next one. Then beat in the yogurt and flour and your filling is done!
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4. Liberally grease the sides of the spring form pan and pour the filling on top of the crust. Use a rubber spatula to smooth out the top. Put the spring form pan into a roasting pan or baking sheet with a large lip. Pour enough water into the outer pan to come 1/4 to 1/2 of the way up the outside of the cheesecake pan. This creates a nice steam that will keep the top from cracking. Be careful not to get water into the cheesecake pan!
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5. Bake the cheesecake in the 350 F oven for about 1 1/2 hours, until cooked through and set. In the meantime, prepare the strawberry topping.
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6. Combine the prepped strawberries, water and sugar in a saucepan over medium heat. Bring it to a low boil and let it cook until the strawberries start to break down and it gets thick, about 10 minutes. Add in the balsamic vinegar and let it heat and thicken for another 3 minutes or so. Then it's done! It is almost is like a strawberry jam but the balsamic keeps it from being overly sweet. Let it cool, then seal it in a container and put it in the refrigerator.
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7. When the cheesecake is done, take it out of the oven and let it cool. Run a knife around the side to make sure it isn't stuck anywhere, and release it from the spring form pan. Carefully slide it onto a cake plate that has a dome and put it in the refrigerator for at least 3 hours to chill, or preferably overnight.
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8. When you are ready to serve it, just pour the strawberry balsamic sauce evenly over the top of the cheesecake, and slice it into the desired sized slices! This is easier to make than people think and it is so incredible!
