In a large bowl, beat the cream cheese and lemon zest until smooth, about 1 minute. Add the vanilla extract. Add 1/2 cup sugar and beat on high-speed until light and fluffy, about 2 minutes. Beat in the eggs one at a time until well blended. Scrape down the sides of the bowl as necessary and make sure everything is well incorporated.
In a medium bowl, whisk together the remaining tablespoon of sugar and cornstarch. Add the berries and toss gently to coat. Place the berries in an even layer over the pre-baked cake layer. Pour the cheesecake layer evenly over the top of the berries.
Bake until cake is lightly golden, and the center is set, 45-50 minutes. Let cool completely, at least 2 hours, before cutting and serving. Serve chilled or at room temperature with a dusting of confectioners sugar.