Make the Lemon Cookies:

1. Pulse lemon zest (2 tablespoons) and granulated sugar (1 ¼ cups) together in a food processor or blender for 10-15 seconds until the zest is finely incorporated.
2. Cream together the lemon sugar and room temperature unsalted butter (1 cup) in a large bowl until light and fluffy, about 2 minutes. Add large egg (1), large egg yolk (1), and fresh lemon juice (3 tablespoons), mixing until well combined.
3. In a separate bowl, whisk together all-purpose flour (3 cups), cornstarch (2 tablespoons), baking powder (¾ teaspoon), baking soda (½ teaspoon), and salt (½ teaspoon). Gradually add the dry ingredients to the wet mixture, mixing until just combined.
4. First Chill: Cover and chill the dough for at least 1 hour (or up to overnight) in the refrigerator.
5. Once the dough has chilled, scoop 50g portions of dough, roll them into balls, and gently flatten each ball slightly.
6. Second Chill: Place the dough balls on the same baking sheet you will use for baking and chill them in the refrigerator for an additional 15 minutes.
7. Preheat the Oven: While the dough chills, preheat the oven to 350°F (175°C). This way, the oven isn't on for over an hour, and everything is ready to bake as soon as the dough is chilled.
8. Once the dough is chilled, bake for 11-13 minutes, or until the edges are set and golden. Let the cookies cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely.

Make the Blueberry Jam Swirled Buttercream Frosting:

1. In a mixing bowl, beat room temperature unsalted  butter (1 cup) on medium speed for about 2-3 minutes until smooth and creamy.
2. Gradually add sifted powdered sugar (4 cups), mixing on low speed to prevent the powdered sugar from puffing up.  Once all the sugar is incorporated, increase the speed to medium and continue to beat for 3-5 minutes, until the frosting becomes light, smooth, and fluffy.
3. Add vanilla extract (1 teaspoon) and start with 3 tablespoons milk. Mix and check the consistency. Gradually add 1 tablespoon of milk at a time until the frosting reaches a smooth, spreadable consistency. You want it thick enough to hold its shape, but smooth enough to spread easily.
4. Add blueberry jam (¼ cup) and mix it into the buttercream. For a swirled effect, mix gently so that streaks of blueberry are still visible. For a solid color, mix until the jam is fully incorporated. Be careful not to over-mix—this will ensure the desired texture and look, whether it's a marbled or uniform color.
5. Once the cookies are completely cool, spread the blueberry jam swirled buttercream on top of each cookie using an offset spatula or butter knife. Gently swirl the frosting with the back of the spatula to create a marble effect. Let the cookies sit for 10-15 minutes before serving.