Cover an 18 X 12 X 1 cookie sheet with aluminum foil. Butter and flour the foil.
Combine first 5 ingredients in food processor. Use one or two on/off turns to mix ingredients. Add butter to processor. Process until fine meal forms. Add white chocolate and process 4-6 times, until chopped. Add toasted almonds and chop coarsely, using 6-8 on/off turns.
Beat eggs in a large bowl. Whisk in brandy and extract. Add flour mixture and apricots to liquid mixture, turning everything over and over with a rubber spatula until moist dough forms,.
Use a spoon to drop the dough into 3 12-inch long strips on the prepared cookie sheet, spacing them evenly. Moisten fingertips with water and gently pat each dough strip into a three-inch wide log. Refrigerate for 30 minutes. (You can refrigerate the logs for a longer period, but if so, cover them with plastic wrap first.)
Preheat oven to 350 degrees F. Bake logs until golden, about 30 minutes. Transfer cookie sheet to rack and cool completely.
Reduce oven heat to 300 degrees F. Transfer one log at a time to a work surface using a large spatula to avoid breakage. Using a heavy, sharp knife, cut each log crosswise into ¾ inch slices. Arrange half of cookies cut side down on an ungreased cookie sheet.
Bake one sheet of biscotti for 10 minutes. Remove from oven and gently turn over cookies. Return to oven, rotating the pan and bake additional 10-12 minutes. Allow to cool on sheet for 5 minutes. Removed biscotti from baking sheet and transfer to a cooling rack. Repeat with remaining cookies. Cool completely.