Spoon 8 portions of lemon curd onto a parchment-lined baking sheet, spacing them about 2 inches apart. Freeze for 1-2 hours until solid—this prevents the curd from leaking out during baking and gives you a defined filling center. While the curd freezes, you'll have time to prepare all your other ingredients.
While the curd freezes, preheat your oven to 350°F and prepare your dry ingredients: whisk together the flour, baking powder, salt, and 1 tablespoon poppy seeds in a small bowl and set aside. Finely zest the lemon (avoiding the white pith) and juice it to get your 1.5 tablespoons lemon juice. Have all ingredients measured and ready before you start mixing the dough—this ensures smooth, efficient mixing and prevents overmixing.
In a mixing bowl, cream together the room-temperature butter, powdered sugar, and sugar until light and fluffy, about 2-3 minutes. Add the egg, egg yolk, lemon juice, lemon extract, and lemon zest from Step 2, beating until well combined. Gently fold in the dry ingredient mixture from Step 2 until just combined—don't overmix, as this keeps the cookies tender. The dough should come together quickly and be slightly sticky but workable.
Divide the dough from Step 3 into 8 equal portions and gently flatten each into a thin disk about 1/4 inch thick. Place a frozen lemon curd center from Step 1 in the middle of each disk, then wrap the dough around it and gently flatten the whole cookie to about 1/2 inch thickness. I like to use my palms to flatten them evenly, rotating the cookie as I press—this creates uniform baking and prevents lumps of dough. Space them 2 inches apart on a parchment-lined baking sheet.
Bake the cookies at 350°F for 12-13 minutes, until the edges are set and just lightly golden but the centers still look slightly underbaked. The cookies will continue to cook slightly after removal and should have a soft, tender crumb. Let them cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely before glazing.
While the cookies cool, make the glaze: melt the 2 tablespoons butter in a small saucepan over medium heat, then add the sifted powdered sugar, 1 tablespoon lemon juice, and 1/2 teaspoon lemon zest. Stir constantly until the mixture simmers and becomes smooth, about 2-3 minutes. Remove from heat and stir in the 1/2 teaspoon poppy seeds and pinch of salt. Once the cookies have cooled completely, use a pastry brush or the back of a spoon to brush or drizzle the warm glaze generously over each cookie. I find that applying the glaze while it's still warm gives the best coverage and shine—let the glaze set for 15-20 minutes before serving.