PREPARATION: Preheat oven to 350 degrees F. Set rack at center. Grease a 9 x 13 baking pan.
MIX DICED APPLES AND LEMON JUICE in a medium bowl and set aside.
WHISK TOGETHER THE WET INGREDIENTS: In a medium bowl, whisk together the oil, milk, eggs, and vanilla. Set aside.
STIR TOGETHER THE DRY INGREDIENTS/ADD WET INGREDIENTS: In a large bowl, stir together the granulated sugar, ½ cup of the brown sugar, the flour, cornmeal, baking soda, baking powder, salt, 1 teaspoon of the cinnamon, ginger, cardamom and allspice. Pour the wet ingredients (milk mixture) into the bowl and mix until just combined.
POUR HALF OF THE BATTER INTO PAN/TOP WITH APPLES, BROWN SUGAR, AND CINNAMON/ADD OTHER HALF OF BATTER: Pour half of the batter (about 2 ¼ cups) into the greased pan and spread evenly. Sprinkle the reserved apples and lemon juice over the batter. Mix the reserved ½ cup of brown sugar and remaining teaspoon of cinnamon in a small cup and sprinkle over the apples. Pour or spoon the other half of the batter on top of the apple mixture and spread evenly with a small offset or skinny rubber spatula. Sprinkle walnuts over the top layer of batter.
BAKE 25-30 MINUTES or until golden brown and a toothpick inserted at the center comes out with a just a few moist crumbs. Begin checking for doneness at 20 minutes. Remove pan to rack and cool at least 20 minutes before cutting and serving from the pan. Cool completely, wrap well, and store a day or two at room temperature or up to a week in the refrigerator. Double wrap and store in freezer up to 3 months.