Beat egg whites till soft peaks form. Gradually add 1/4 cup sugar and beat till stiff peaks form. Set aside.
In large bowl, cream butter and 3/4 cup sugar. Beat in vanilla. Stir in dry ingredients and gumdrops. (Mixture will be very dry.) Gently stir in the beaten egg whites.
Drop dough by spoonfuls onto silpat or parchment lined cookie sheets. Bake at 350° for about 10 minutes. Cool for 2 minutes before removing to cooling racks.