Via The Kitchen with only a few changes. Very moist with a soft, pudding like center especially if you choose to grate the apples instead of cutting into chunks. Pears are a good substitute for the apples if you want to try a variation.
Preheat oven to 350 degrees. Lightly grease a 9x13-inch baking pan with butter or oil.
In a large non-reactive bowl whisk together the plain yogurt, olive oil, orange zest and juice, 3/4 cup sugar, eggs and vanilla.
Peel and core the apples and shred (used a food processor) or cut into chunks. I prefer to shred the apples. You will need about 3 1/2-4 cups of apples. Stir the apples into the yogurt mixture.
Combine the flour, baking powder, baking soda, salt, 1 teaspoon ground cinnamon, nutmeg, and cardamom then stir into the liquid ingredients stirring until no lumps remain.
In a small prep bowl, mix together the remaining teaspoon of ground cinnamon with the brown sugar and butter.
Pour [half] of the batter into the prepared cake pan. Sprinkle the batter with [half] of the cinnamon-brown sugar mixture, dropping it on the batter in small lumps. Spread the rest of the batter over the top, and sprinkle with the remaining cinnamon-brown sugar.
Bake for about 50 minutes covering the cake with aluminum foil at the end if the top is browning too quickly. Test the center with a toothpick then transfer the cake to a cooling rack and allow to cool for at least 15 minutes before cutting. Serve the cake warm or at room temperature. Delicious with tea or coffee!