Preheat the oven to 350° F (180° C) and line an 8x8 (20cm) pan with parchment.
Make the cake layer: in a medium bowl, stir together the flour, baking soda, and salt. In a large bowl, with an electric mixer, cream together the butter and sugar at medium speed until fluffy. Add the vanilla, lemon juice, and egg, and mix until they are fully incorporated.
Add half the flour mixture and mix gently on low, then mix in all of the milk, and lastly add the second half of the flour. Mix on low until the flour is just incorporated, scraping the sides of the bowl and taking care not to overmix. Spread the batter in the bottom of the parchment-lined pan. The batter should be very thick.
Make the cream cheese layer: In a large bowl, with an electric mixer, whip the cream cheese on medium speed until fluffy. Add the salt and powdered sugar and continue mixing until they are fully incorporated, scraping the sides of the bowl. Finally, add the egg and the lemon zest and mix until it becomes smooth.
Pour the cream cheese mixture on top of the cake batter, spreading it with a spatula until it reaches the edges. Sprinkle the blueberries on top and press them lightly into the cream cheese. Transfer to the oven and bake for about 50-60 minutes, until the top is lightly browned all over.
Because they contain cream cheese, the chess squares will store best in the refrigerator for up to 4-5 days.
