Preheat the oven to 300 F with a rack in the center of the oven.

Whisk together the flour, cocoa powder, baking powder and salt. Remove about 1/4 cup and place it in the food processor with the blade attached. Set the rest aside.

Add the bittersweet chocolate to the food processor with the flour mixture and process until completely pulverized. Add back to the flour mixture.

Cream the butter and sugar together until completely integrated and creamy. Mix in the eggs and vanilla--if using a mixer, mix on speed 2 or lower. Add the flour and mix on the lowest speed, just until all of the flour has been evenly moistened by the butter-egg mixture.

Stir in the peppermint baking chips and the white chocolate. Place parchment or a silicone mat on a cookie sheet. Shape the dough on the cookie sheet to form a long rectangle, about 16X4 inches for long biscotti, or 2 shorter and more narrow logs for shorter biscotti.

Bake for approximately 35 minutes (start checking at 20 minutes if baking 2 logs), until the loaf is firm but springy to the touch. Rotate from front to back halfway through to ensure even baking. Obviously do not let the loaf burn, but in light of my experience with a loaf that was almost too soft to slice, I would err on the side of overbaking. At 300 F this is not too risky.

Remove the loaf to cool on the pan. Let it cool for at least 2 hours and up to overnight. Before slicing, turn the oven back on to 300 F. Remove the loaf or loaves–carefully!–to a cutting board. Slice 1/2-inch slices of the loaf and transfer them back to the cookie sheet, placing them 1/2 inch apart. If you need to, use 2 cookie sheets and place the oven racks in the lower and upper third of the oven.

Bake for an additional 35 minutes, until the biscotti feel dry and crusty (they will not feel perfectly hard though, that will happen as they cool). Rotate from front to back (and top to bottom if using 2 sheets) halfway through. Cool the biscotti completely before storing in airtight tins.