Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper or leave them ungreased if preferred.

In a large mixing bowl, combine the shortening and ¾ cup of sugar. Beat with an electric mixer on medium speed until light and fluffy, about 2–3 minutes. Blend in the almond extract until incorporated.

In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry mixture to the creamed shortening mixture, mixing just until combined.

Stir in the chopped gumdrops, ensuring they are evenly distributed throughout the dough. Lightly flour them before mixing if they tend to stick together.

In another clean bowl, beat the egg whites until soft peaks form. Gradually add the remaining ¼ cup sugar, continuing to beat until stiff peaks form. Gently fold the whipped egg whites into the cookie dough until evenly combined.

Drop tablespoonfuls of dough onto the prepared baking sheets, spacing them approximately 2 inches apart. Bake for 12–15 minutes, or until the edges are lightly golden.

Allow the cookies to cool on the baking sheet for 2–3 minutes before transferring them to a wire rack to cool completely. Once cooled, store in an airtight container for up to one week.