In a large pot over medium heat, add all ingredients for the veal cheeks. Bring mixture to a boil. Reduce heat and let simmer until veal is fork-tender, skimming surface of any impurities that arise. Remove from heat and transfer mixture into a large nonreactive container. Let cool.

In a sauté pan over medium heat, melt butter for the Vin Jaune Sauce. Add shallots and mushrooms and sweat until shallots are soft and translucent. Deglaze pan with wines and cook until au sec, stirring constantly. Stir in cream. Reduce heat to low. Cook until mixture has reduced by twenty-five percent. Remove from heat and let steep 10 minutes. Strain into a nonreactive container set over an ice bath. Let cool.

Heat oven to 400°F. In a sauté pan over medium heat, melt butter for the spring onions. Add onion bottoms, cut-side-down. Cook until onions are slightly browned. Deglaze pan with vin jaune. Season with salt. Transfer pan to oven and cook until onions are fork-tender. Transfer to a nonreactive container and reserve.

On a lightly floured work surface, lay out 1 sheet puff pastry. Brush with egg wash. Set aside. Lay out the second sheet puff pastry. Using 70-millimeter ring cutters, punch out rounds. Lay rounds on top of the eggwashed puff pastry. With the remaining dough, use 90-millimeter ring cutters to punch out rounds. Place rounds over top of smaller rounds. Transfer pastries to a sheet tray and freeze. Once frozen, bake 20 minutes. Let cool.

In a pot over medium-low heat, warm Veal Cheeks. Season with salt. In a separate pot over medium-low heat, warm Spring Onions. Season with salt. In a separate pot over medium-low heat, warm Vin Jaune Sauce. Season with salt. On a work surface, use a paring knife to cut out the center of a Vol-au-Vent. Add desired amount of warm Veal Cheeks and Spring Onions to the center of the Vol-au-Vent. Top Vol-au-Vent with desired amount of Spring Onions. Pour warm Vin Jaune Sauce over top. Finish with flaky salt.