Prepare tart crust. . Preheat oven to 425 degrees F. On a lightly floured surface roll dough to a 16x8-inch rectangle about 1/8-inch thick. Press pastry into a 14x41/2-inch rectangular tart pan with a removable bottom; trim edges. Line with a double thickness of aluminum foil. Chill 15 minutes. Place on a large baking sheet.
Bake for 8 minutes. Remove foil; bake 8 minutes more or until just golden brown. Cool on baking sheet on a wire rack. Reduce oven temperature to 350 degrees F.
Meanwhile, in a very large nonstick skillet, cook onions in 1 tablespoon hot olive oil over medium heat about 3 minutes or until a rich golden hue, stirring occasionally. Add 1 tablespoon water; sprinkle with salt. Cover; cook just until tender, about 2 minutes more. Remove from skillet; set aside. Discard any liquid.
In the same skillet heat remaining olive oil over medium-high heat. Add mushrooms; cook for 6 minutes or until tender, stirring occasionally. Sprinkle lightly with salt and pepper. Remove from heat and cool; set aside.
In a small bowl whisk together creme fraiche, egg yolks, and cooled melted butter. Set aside.
In pastry-lined tart pan evenly arrange mushrooms and onions. Slowly pour creme fraiche mixture into tart pan. Bake on the baking sheet for 40 minutes or until filling is set and top is golden. Cool on wire rack. Remove sides from tart pan. Sprinkle with shaved Parmesan cheese and baby arugula, if desired. Serve warm or at room temperature.