Add the sugar and lemon zest to a large mixing bowl or the bowl of a stand mixer. Gently crush and mix the lemon zest into the sugar using your fingers until the sugar becomes fragrant.
Add the sugar mixture, softened butter and vanilla extract. Beat well until the mixture becomes light and fluffy.
In a separate bowl, combine the all-purpose flour, baking powder, and salt.
Add the dry ingredients to the mixer and mix just until combined.
Prepare the egg replacer according to the package instructions, using enough to replace 2 eggs. Add it to the mixer and mix until combined.
Divide the cookie dough into three equal portions. Flatten the first portion of dough in the bottom of the mixing bowl. Spoon a little of the blueberry or blackberry jam over the dough.
Place the second portion of dough over the first layer and add another spoonful of jam. Add the third and final portion of dough and top it with the remaining jam. Using a spatula or fork, gently mix the layers just enough to create a marbled effect. Do not mix completely.
Scoop the dough using a cookie scoop and gently roll it into balls. Place the sugar for coating in a small bowl. Roll each cookie dough ball in the sugar and arrange them on a baking sheet lined with parchment paper.
Using the back of a measuring spoon, gently make a sufficiently deep indentation in the center of each cookie dough ball for the cream cheese filling.
Preheat the oven to 350°F.
While the oven is preheating, prepare the cream cheese filling. Add the softened cream cheese, sugar, and vanilla extract to a mixing bowl. Mix well until combined. Add the heavy cream and continue mixing until smooth and free from lumps.
Spoon the prepared cream cheese filling into the indentation in the center of each cookie. Bake on the middle rack for 12–15 minutes, or until the cream cheese center sets, the cookies puff up, and the edges appear baked.
While the cookies are baking, add the blueberries, lemon juice, and sugar to a saucepan. Cook over medium heat, stirring frequently, until the blueberries begin to soften and release their juices.
In a small bowl, mix the cornstarch and water to form a smooth slurry. Once the blueberries become soft and slightly mushy, add the cornstarch slurry. Mix well and cook for another minute or two, until the blueberry mixture becomes thick and glossy. Turn off the heat and allow the topping to cool completely.
Leave the cookies on the baking sheet until they cool completely and reach room temperature. The cookies will be extremely soft immediately after baking. Do not transfer them to a cooling rack. Once both the cookies and blueberry topping have cooled to room temperature, spoon the blueberry topping over the cream cheese center and serve.