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Preheat the oven to 350 degrees F. Butter a 9x13-inch baking dish.
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Combine 1 1/2 cup flour and confectioners' sugar in a mixing bowl. Cut in cold butter with a pastry blender or a knife until mixture resembles coarse crumbs. Press crumbs into the bottom of the prepared baking dish.
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Bake until lightly golden brown, about 15 minutes. Remove from oven, and set aside while you work on the fillings.
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For the lemon layer, whisk together 4 eggs, 1 1/2 cup sugar, 1 tablespoon flour, lemon juice, and lemon zest in a bowl. Pour the mixture into prepared crust. For the cheesecake layer, mix cream cheese and 1 cup sugar in a bowl until well blended. Whisk in 2 eggs and vanilla, then spread gently over lemon mixture. If it looks like they are blending together, don't worry. The layers will separate during baking.
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Bake until the filling is set, about 30 minutes.