Prepare 2 baking sheets by lining with parchment paper, a silicone mat, or spray with non-stick spray.
In a large bowl, combine the cake mix, melted butter, eggs, and lemon zest with a wooden spoon until well mixed. It will seem dry at first, but the dough will come together. Let the dough rest for 10 minutes.
Lightly dust your hands with flour to help keep the dough from sticking. Then roll the dough into 1-inch balls (about 1 tablespoon). Place the dough balls about 2 inches apart on the prepared baking sheets.
With your thumb or the back of the cookie scoop, gently press the center of each dough ball to form a divot for the jam. Scoop about one teaspoon of jam into each cookie. Then place the tray in the fridge for 10 minutes to chill.
While cookies are chilling, preheat your oven to 350 degrees F.
Bake for approximately 15 minutes on the middle rack. The cookies should feel slightly set on the edges and the bottoms should be lightly browned.
Remove from the oven and allow to cool for 5 minutes on the pan. Then move to a cooling rack to cool completely.
Glaze
In a small bowl, mix the powdered sugar with 3-4 teaspoons of lemon juice. You are looking for it to be thick, but have a pouring consistency, like honey.
When the cookies have cooled, drizzle the icing on top with a spoon or a small ziplock bag with the tip of a corner cut off.
Notes
If you don't have salted butter on hand, add 1/4 teaspoon salt and use unsalted butter.
I used the French vanilla cake mix for this recipe as it gives the cookies more of a sugar cookie flavor, but yellow or confetti cake mix would be good too.
The resting and chilling steps are both important steps that help hydrate the cake mix creating better texture.
If you don't want lemon-flavored glaze, swap out the lemon juice for milk instead.