Lightly coat the seitan cutlets in flour, shaking off any excess.
Heat the olive oil in a large skillet over medium-high heat.
Add the floured seitan and cook for 1-2 minutes per side, pressing down gently to ensure they brown evenly.
Remove the seitan from the skillet and set aside, keeping it warm.
To the same skillet, add the sliced mushrooms, chopped onion, and minced garlic.
Sauté for 7-10 minutes until the vegetables are softened and have a nice golden-brown color.
In a small bowl, whisk together the red wine, Dijon mustard, and dried thyme.
Pour this mixture into the skillet with the mushrooms.
Season with salt and pepper to taste.
Bring to a simmer and cook for 2-3 minutes, allowing the sauce to reduce and thicken slightly.
In the same small bowl, whisk the cornstarch into the vegetable broth until smooth.
Pour this slurry into the skillet, stirring constantly.
Continue to simmer for another 2-3 minutes, stirring, until the sauce has thickened.
To serve, place the warm seitan cutlets on plates, spoon the mushroom red wine sauce over the top, and garnish with fresh chopped parsley.