Position a rack in middle of oven; preheat to 350°F. Line a large baking sheet(s) with parchment paper.
Whisk all-purpose flour, whole-wheat flour, cinnamon, ginger, baking powder, cloves and salt in a medium bowl.
Beat oil, butter, brown sugar, molasses, egg and orange zest in a mixing bowl with an electric mixer on low speed until well blended.
With the mixer on low speed, then medium speed, beat about half the flour mixture into the wet ingredients until incorporated.
Beat in the remaining flour mixture until just incorporated. Let the dough stand for 5 minutes. It should be somewhat firm, but not at all dry. If it seems overly sticky, stir in up to 2 additional tablespoons of all-purpose flour.
Divide the dough into quarters. Roll each quarter into a 9-inch “log.” Slice the log into 12 equal pieces. Roll each piece of dough into a ball.
Place crystalized ginger on a small plate. Roll each ball in the ginger, pressing as needed to help it adhere. Place about 1 1/2 inches apart on a prepared baking sheet. Press a well into the center of each cookie with a thumb. Fill with about 1/2 teaspoon jam.
Bake the cookies on the center rack, one pan at a time, until firm when pressed near the edge, 8 to 12 minutes. Let stand for 5 minutes, then transfer to wire racks to cool to room temperature.