Preheat the oven to 350°. Spray a 13x9 baking pan with cooking spray. Set aside.
In a small bowl, whisk the flour, baking powder, baking soda, salt, cinnamon, ginger, and allspice together until well blended.
Whisk the oil, sugar, and brown sugar together in a separate large bowl until fluffy.
Add the eggs, individually, and whisk until the eggs are just mixed. Be careful not to over-mix.
Stir in the pumpkin puree and Greek yogurt.
Fold in the dry ingredients until just mixed. Some small lumps in the batter are fine. The batter should be thick but pourable.
Pour the batter into the 13x9 pan, and spread it out evenly. Bake for 20-25 minutes, or until the edges are golden brown and a toothpick poked in the middle of the cake comes out clean. Set on a cooling rack to rest.
In a large bowl, use an electric hand mixer to mix the cream cheese, butter, and vanilla extract.
Pour in about half of the confectioners sugar, and continue mixing. Pour in the second half of the sugar and mix until smooth.
Once the cake has cooled to room temperature, spread the frosting over the cake with a spatula, and sprinkle the pecan pieces on top.