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

Lower the temperature to medium-low and let the mixture simmer gently for about 10 minutes, until the berries have softened and popped. Remove from heat and allow to cool completely.

Heat the oven to 350°F. Lightly grease a 9-inch pie dish or a 9-inch tart pan with a removable bottom.

In a bowl, mix the flour, sugar, baking powder, and salt. Work in the cold butter with a pastry blender or two forks until the mixture resembles coarse crumbs and clumps together when squeezed. Measure out 1/2 cup of this crumb mixture and set aside for the topping.

Press the remaining crumb mixture evenly and firmly onto the bottom and up the sides of the prepared pan. Bake for 10 minutes, then let it cool on a wire rack while you make the filling.

In a large mixing bowl, beat the softened cream cheese and sugar with an electric mixer on medium speed until smooth and creamy. Blend in the egg and vanilla, scraping down the bowl, until fully combined and silky.

Pour the cheesecake batter over the cooled prebaked crust and spread it into an even layer.

Gently drop spoonfuls of the cooked cranberry mixture over the cheesecake, leaving a 1/2-inch border uncovered at the edges.

Sprinkle the reserved crumb topping evenly over the cranberries.

Bake for 30 to 35 minutes, until the edges are lightly browned and the center no longer jiggles when the pan is gently shaken. Let cool to room temperature, then cover and refrigerate for at least 2 hours (overnight is even better). Serve chilled.