Preheat the oven to 375°F and position a rack in the center of the oven.

Cut the 14 yellow gumdrops into thirds and set the pieces aside.

In a large bowl, beat 1/2 cup (1 stick) butter at room temperature on medium speed with an electric mixer for 30 seconds.

Add 3/4 cup granulated white sugar, 4 teaspoons finely grated lemon zest, 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/8 teaspoon salt. Beat on medium speed until combined, scraping down the sides of the bowl occasionally.

Add 1 large egg, 1/2 cup sour cream, and 1/3 cup freshly squeezed lemon juice. Beat until the mixture is uniform.

Add 2 cups all-purpose flour to the bowl. Beat with the mixer as much of the flour as you can, then finish stirring in any remaining flour with a spatula until just combined. Do not overmix.

Drop the dough by slightly rounded tablespoons onto an ungreased cookie sheet, spacing the drops about 3 inches apart.

Gently press one gumdrop piece (one of the thirds) into the center of each cookie. Use remaining gumdrop pieces as desired.

Bake the cookies for 10 to 11 minutes, or until the tops are firm and the edges are set.

While the cookies bake, make the lemon glaze: warm 2 tablespoons freshly squeezed lemon juice a little (warm but not hot) and stir it together with 1/4 cup granulated white sugar in a small bowl until the sugar begins to dissolve.

Transfer the baked cookies to a wire rack. Brush the tops of the warm cookies with the lemon glaze.

Let the cookies cool on the wire rack before serving.