For the gravy: Cook the bacon in a large skillet over medium heat until crispy and most of the fat has been rendered, 10 to 12 minutes. Transfer to a paper-towel-lined plate to absorb any excess fat and set aside.
Add the onions to the pan and cook until softened, 4 to 6 minutes, and then stir in the mushrooms and thyme and cook until the mushrooms are just cooked through, 4 to 6 minutes longer. Stir in 1/4 cup of the beef stock to combine, and then stir in the flour to combine and cook for 2 to 3 minutes. Add the remaining stock and bring to a boil over medium-high heat, and then reduce to a simmer and cook, stirring frequently, until the sauce is thickened to the consistency of gravy, 6 to 8 minutes. Cover and set aside.
For the wiener schnitzel: Place each veal cutlet in between two pieces of plastic wrap. Pound each one using the spiky side of a meat mallet to tenderize it. Lightly season with salt and pepper.
Set up the breading station. Whisk together the flour, 1/4 teaspoon salt and 1/4 teaspoon pepper in a shallow baking dish, and whisk together the mustard and eggs in another shallow baking dish. Combine the breadcrumbs with 1/4 teaspoon salt and 1/4 teaspoon pepper in a third baking dish.
Dredge each veal cutlet first in the flour, then through the egg mixture, and lastly through the breadcrumbs. Transfer onto a baking sheet lined with a cooling rack and refrigerate for 15 minutes.
Preheat the oven to 300 degrees F. Heat 2 tablespoons of the oil over medium-high heat in a large cast-iron skillet. Melt 2 tablespoons of the butter into the oil until it starts to bubble, and then add 1 of the breaded veal cutlets and cook until golden brown on both sides and cooked through, flipping once and moving the pan constantly, 3 to 4 minutes total. Transfer to a baking sheet lined with a cooling rack, season with salt and pepper and keep warm in the oven. Cook the remaining cutlets, making sure to wipe out the pan and use new oil and butter each time. Keep adding the finished veal cutlets to the baking sheet in the oven as you cook them.
To serve, top the wiener schnitzel with the gravy, reserved bacon, and parsley.