Stir together flour, baking soda, baking powder and salt. Set aside.
With an electric mixer, beat butter and sugar together until creamy. Add eggs and extracts; beat on low speed for about 10 seconds.
Using lowest speed of mixer or by hand, stir in flour mixture. When flour is incorporated, stir in cherries, almonds and white chocolate. Chill dough for about 2 hours.
Preheat the oven to 350 degrees F. Drop by rounded teaspoonfuls onto ungreased cookie sheets. Place on center rack of preheated 350F oven, and bake 10 to 12 minutes, or until light golden brown. Cool slightly before removing from cookie sheet.