1. Preheat oven to 375°.
2. In a large bowl, combine butter and sugars; beat with an electric mixer until fluffy. Add oil and eggs; beat until creamy. Stir in vanilla.
3. In a medium bowl, combine flours, baking powder, and salt. Add flour mixture to butter mixture; stir well. Gently fold in chocolate, cherries, and almonds.
4. Scoop batter by heaping tablespoons onto 2 baking sheets covered with parchment paper. Bake cookies in 2 batches in upper and lower third of oven until golden on top and bottom (12-15 minutes). Transfer cookies on parchment paper to a wire rack; cool (cookies will crisp as they cool). Store cookies at room temperature in an airtight container (they will keep for up to 4 days).