Make the cookies. Preheat oven to 350 degrees F. Line a cookie sheet with parchment. In a medium bowl, stir together flour, baking powder, and salt. In a large bowl, cream sugar and butter until light and fluffy. I did this by hand, but a hand or stand mixer would work as well. Add the eggs and mix until once again light and fluffy. Add the vanilla and mix to combine.
Add the flour and mix just until a dough is formed. Using a regular sized ice cream scoop, scoop dough onto prepared pan. Bake for 17-20 minutes, until cookies are golden brown around the edges and just starting to set. While cookies are hot, use your thumb to make a large indentation in the center of the cookies. Cool completely on tray. Cookies may be made 1 day ahead of time.
Lemon Curd and Meringue Topping
Make the lemon curd. In a medium saucepan, whisk together lemon zest and juice, sugar, and egg yolks. Place the pan over medium-low heat and cook, stirring constantly, until the curd thickens slightly, about 5-7 minutes.
Remove the pan from the heat and stir in the butter 1 piece at a time. Continue stirring until all the butter is emulsified. You may strain the curd if you like. I skipped that step. Pour the curd into an airtight container and place a piece of plastic wrap directly on top of the curd to prevent a skin from forming. Store curd in the refrigerator for up to 1 week.
Make the meringue. In a small saucepan, combine water, sugar, and corn syrup over medium heat. Stir frequently until the sugar is dissolved and the mixture is clear. Once this happens, attach a candy thermometer, raise the heat to medium-high, and stop stirring. Allow the mixture to come to 240 degrees F on the candy thermometer.
In the meantime, in the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites on medium-high until frothy. Add the cream of tartar. Continue beating on medium-high until the egg whites form stiff peaks.
When the egg whites have formed stiff peaks and the sugar mixture has reached 240, remove the syrup from the heat and turn the mixer to medium-low. Slowly and immediately begin drizzling the syrup into the egg whites, trying not to get it on the sides of the bowl. If the whites are done whipping before the syrup is done, turn them off until the syrup reaches 235, then turn them back on to make sure they are fluffy. If the syrup is done before the whites, turn the heat down or remove it from the heat for a minute or so.
Once the syrup is drizzled into the whites, turn the mixer back up to medium-high and beat for about 7 minutes, until the bottom of the bowl is cool and the marshmallow is thick, glossy, and voluminous. Add the vanilla and mix about 1 minute more. Meringue may be stored in the refrigerator for up to 2 days.
Assemble the cookies. Generously fill the indentation in each cookie with lemon curd. Place several mounds of meringue on top and smooth with an offset spatula, covering cookie entirely. Once all the cookies are coated, turn on the broiler and broil until the meringue is golden brown. Cookies may be stored in the refrigerator for up to 2 days.