Make crust: Combine flour and sugar in the bowl of a stand mixer, or other large bowl. add a good pinch of salt. Cut the butter and shortening into tablespoon pieces and drop in. Use the paddle beater to cut the butter, shortening, and flour together. Alternatively, this can be done by hand with a pastry blender.
With the mixer on low speed , or while stirring the mixture with a fork, pour in the cold water. When the dough starts to clump, and before it turns into a ball, stop stirring.
Lightly knead dough in the bowl until it forms a ball. Divide dough into two parts. Flatten each part into a disk, wrap in plastic wrap or waxed paper, and chill for about 30 minutes before rolling.
Make tart filling: Preheat oven to 400° Combine the squash, onion, and sage in a bowl, pour in olive oil, and toss to coat well. Season with coarse salt and ground pepper. Spread in a thin layer on a baking sheet and roast until the onions and the squash have caramelized edges.
Assemble tarts: Roll out the crust and fit it into two 8 or 9 inch fluted tart pans with removeable bottoms. Sprinkle half the parmesan into each crust. Divide the squash mixture between the two pans. Sprinkle the goat cheese on top of the squash. Beat the eggs, egg yolks, cream and half & together and pour over. Place the tart pans on a baking sheet, place in the oven, and immediately turn the heat down to 375°. Bake for about 35 minutes until puffed and golden.