For the Squash Bottom
Preheat oven to 350°. Butter and flour a 10-inch round cake pan. Line the bottom with parchment paper.
In a small saucepan put 8 tablespoons butter and the brown sugar over medium heat. Whisk and cook until smooth. Pour into the lined cake pan. Cut squash lengthwise, scoop out seed and cut into half moons 1/4-inch thick. Shingle beautifully on top of the brown sugar layer.
For the Cake
In a medium bowl sift together the 1 3/4 cups flour, baking powder, nutmeg and salt. In another medium bowl, whisk together 7 tablespoons melted butter with the olive oil and milk.
In a large bowl, using a handheld mixer, beat the eggs with the sugar and lemon zest until ribbons begin to form (pale and thick), about 10 minutes. Alternately, beat in the dry and wet ingredients, beginning and ending with the wet ingredients. Pour the batter over the squash in the prepared pan. Bake for 75 to 90 minutes. If it seems to be browning too fast after 1 hour, reduce heat to 325° for the remainder of the time.
For an over the top presentation, garnish with additional slices of delicata squash gently poached in simple syrup, if desired.