Heat the oven to 350°F (175°C) and line baking sheets with parchment paper. Chop the gumdrops finely with lightly greased kitchen shears or a greased knife, then toss them with a light dusting of flour from the measured amount.

Cream the softened butter, granulated sugar, and packed brown sugar in a large bowl until the mixture is light and fluffy. Beat in the eggs one at a time, mixing well after each addition, then blend in the vanilla.

Whisk together 3 cups of flour, the baking soda, and salt in a separate bowl. Gradually add the dry ingredients to the butter mixture, mixing only until the dough comes together; add some of the remaining flour only if the dough is too loose to scoop.

Fold in the chopped gumdrops gently so the candy pieces stay distributed through the dough. Chill the dough for 20 to 30 minutes if you want thicker, softer cookies.

Drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between portions. Bake for 10 to 12 minutes, watching for lightly golden edges and centers that still look soft.

Cool the cookies on the baking sheet for 5 minutes before transferring them to a wire rack. They will firm as they cool while keeping their pleasant chewy texture.