In a heavy-bottomed saucepan, stir together the fresh cranberries, granulated sugar, Meyer lemon zest, Meyer lemon juice, and water. Bring the mixture to a boil over medium-high heat.

Reduce the heat to medium-low and let the cranberries simmer gently for about 10 minutes, until they have burst and softened. Remove the pan from the heat and allow the filling to cool completely.

Preheat the oven to 350°F. In a medium bowl, whisk together the flour, granulated sugar, baking powder, and salt. Add the cold butter pieces and work the mixture with a pastry blender or two forks until it becomes coarse, crumbly, and holds together when pinched. Set aside 1/2 cup of this crumb mixture for the topping.

Transfer the remaining crumb mixture into a 9-inch pie pan or a 9-inch tart pan with a removable bottom. Press the mixture firmly and evenly across the bottom and up the sides of the pan.

Bake the crust for 10 minutes, then set it aside to cool slightly while you prepare the cheesecake filling.

In a large mixing bowl, beat the softened cream cheese and granulated sugar with an electric mixer on medium speed until light and fluffy. Add the egg and vanilla extract, and continue mixing until the filling is completely smooth.

Pour the cheesecake filling over the slightly cooled crust and spread it into an even layer.

Drop the cooled cranberry mixture by teaspoonfuls over the cheesecake filling, leaving about a 1/2-inch border around the edges of the crust.

Crumble the reserved crust mixture evenly over the top of the cranberries.

Bake the pie for 30 to 35 minutes, until the edges are golden brown and the cheesecake filling is set in the center.

Let the pie cool completely on a wire rack, then cover and refrigerate for at least 2 hours before slicing and serving. Keep the pie stored in the refrigerator.