Preheat oven to 375° F. Line baking sheets with parchment paper.
In a small bowl, whisk together the flour, baking soda, baking powder, and sea salt. Set aside.
In another small bowl, whisk together the sour cream, milk, vanilla, and lemon juice. Set aside.
In the bowl of an electric mixer, press the lemon zest into the sugar with your fingertips. Using the paddle attachment of a stand mixer, add the butter and cream until light and fluffy, 2-4 minutes. Beat in the eggs, one at a time, until fully incorporated, and the mixture continues to be light and fluffy. You may have to stop the mixer once or twice to scrape down the sides of the bowl.
Turn the mixer off and add a third of the flour mixture. Turn the mixer back on low. Before the dry ingredients fully disappear, add half of the sour cream mixture. Repeat with another third of the flour, the rest of the sour cream mixture, and the rest of the flour. You are done mixing once you can no longer see any of the flour. Do not overmix. With a rubber spatula, fold in the blueberries.
Use a medium cookie scoop to scoop the batter onto the prepared baking sheets, spacing them at least 2 inches apart. (You can bake two sheets at a time on different shelves, rotating them and exchanging them on the shelves in the oven half way through. Or you can bake one sheet at a time. The dough can remain at room temperature in the mixing bowl until you have scooped and baked them all.) Bake for 6 minutes, rotate the sheets, and bake an additional 4 minutes. The cookies will not brown on top, will look almost uncooked in the middle, and be just slightly browned on the bottom. They will continue to firm up while cooling.
Transfer baking sheets to wire racks and let cool for 5-10 minutes, then transfer the cookies directly to the wire racks to cool completely while you make the glazes.
Glazes. Place the confectioner’s sugar in a medium bowl. Add the corn syrup and salt. Whisk in 1 Tablespoon of boiling water. The consistency will seem too thick. Pour a little less than half the glaze into another bowl. Into the original bowl (with more glaze), add the lemon juice and lemon zest, whisking until fully combined. If it is too thick, add 1 teaspoon of boiling water at a time until it is a thick but spreadable consistency. In the other bowl, whisk in all of the blueberry paste. If the blueberry icing is too thick, whisk in an additional 1 teaspoon of boiling water as necessary for a thick, spreadable consistency.
Assembly. Flip each cookie over. Using a spoon or a spatula, spread the lemon glaze over half of each cookie. Then spread the blueberry glaze over the other half of each cookie. Place on wire rack until the glazes are fully set.