While the cheesecake is baking make the topping: In a medium sized bowl, stir together the yogurt, sugar and vanilla. Set aside at room temperature until cheesecake is baked.
Once the cheesecake is baked, remove it from the oven. Gently spoon the topping over the still hot cheesecake in several additions. The cheesecake will still be fragile while it is hot, so you want to work gently as to not break through the top. Using an offset spatula, spread the topping over the cheesecake.
Bake for 8 more minutes, no longer.
Remove from oven, immediately run a knife, dipped in hot water, around the edge of the pan, just about 1/2-inch-deep. This will help to prevent the cake from cracking and will make removing it easier once it is fully cooled. Cool to room temperature, then refrigerate in the pan for several hours or overnight. Once the cake is thoroughly chilled. Run a knife, dipped in hot water, around the cake again, this time going a bit deeper into the pan, about 2-inches. Release the springform pan and move the cake to a serving platter.
Add fresh berries to the top and serve. The cake can be made a day or two ahead.