Preheat oven to 350.
In a large bowl, whisk eggs with maple syrup, sugar, butter, milk, vanilla, and pumpkin.
In another bowl, mix remaining dry ingredients.
Mix the dry into the wet, about a cup at a time. In a 8x8 greased dish (or parchment lined) spoon in batter. Bake for 40 minutes, until knife inserted in center comes out clean. Cool completely. .
While cake is cooling, make frosting. Start by beating together the butter, cream cheese, and vanilla. Add powdered sugar and beat until fluffy. Start with 1 cup. Slowly add more until you reach the sweetness and consistency you want. It varies according to preference, but I usually add about 1 cup. Spread over cooled cake