Preheat the oven to 350 degrees F. Line a 9x13-inch baking pan with parchment paper, then lightly coat with baking spray.
In the bowl of a standing mixer fitted with the paddle attachment or a large mixing bowl, beat together the oil, Greek yogurt, brown sugar, and honey until well blended and smooth. Beat in the eggs, one at a time, incorporating between each. Beat in the pumpkin puree.
Sprinkle the baking soda, baking powder, salt, and pumpkin pie spice over the top. Mix to combine. Then, sprinkle in the whole wheat flour and all-purpose flour. By hand with a wooden spatula or spoon, stir the batter, just until the flour disappears.
Pour the batter into the prepared pan, then with an offset spatula or spoon, smooth the top. Bake for 30-35 minutes, until a toothpick inserted in the center comes out clean. Place the cake on a wire pan to cool completely.
To make the frosting: In a medium bowl, beat together the cream cheese, Greek yogurt, butter, vanilla extract, and salt at medium speed for 2 minutes, until fluffy and well combined. Reduce the mixer speed to low and gradually add the powdered sugar, increasing the speed to medium as you go. Beat for 1-2 minutes until well combined. Spread frosting evenly over top of cooled cake. Let the frosting set for 10 minutes (you can pop the cake into the refrigerator if you are in a hurry), then slice and serve.
Notes
TO STORE: Cover and refrigerate cake for up to 4 days.
TO FREEZE: Freeze cake in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before serving.