Preheat oven to 350 degrees F.
In a mixer, beat the butter and brown sugar until blended. Beat in the egg and vanilla and almond extracts until combined. Add the flour, baking soda, and salt, and mix until combined. With a wooden spoon, mix in the apricots and white chocolate. Drop the batter by tablespoons onto ungreased cookie sheets, spacing 2 inches apart. Bake until the edges are lightly brown, about 10 minutes. Cool on wire racks.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.