Step 1In a small jar, combine the diced dried apricots and figs with the wine. Close the jar and shake a few times to moisten the fruit, then set the mixture aside for 30 minutes while preparing the remaining ingredients.
Step 2Heat the oven to 350 degrees. Lightly butter an 8-inch square baking pan. Line the pan with foil and butter the foil.
Step 3In a medium bowl, mix the matzo cake meal, potato starch and salt.
Step 4In a large mixing bowl using a hand-held mixer, or in a stand mixer, beat the butter until it is smooth. Add the oil and the granulated and brown sugars; beat until the mixture is smooth and fluffy. Add the haroset and beat on low speed until blended. Add the eggs, one by one, beating thoroughly on high speed after each one. Add 4 tablespoons of the matzo meal mixture and beat over low speed. Using a wooden spoon, stir in the remaining matzo meal mixture. Stir in the dried fruit mixture and any wine in the jar. Stir in the chocolate pieces.
Step 5Transfer the batter to the pan and spread it in an even layer. Sprinkle over the chopped walnuts and pat them lightly so they adhere to the batter. Bake until the top browns lightly and a wooden pick inserted into the center comes out nearly clean, 18 to 22 minutes; if the wooden pick comes out chocolaty, test again. Cool the cake in the pan on a rack.
Step 6Turn the cake out gently onto a plate, then onto another plate or a cutting board so that the walnuts are on top. Using a sharp knife, cut it carefully into 16 bars. Serve at room temperature.