Season the chicken schnitzel with salt and pepper. Heat 2 teaspoons oil in a large pan over medium-high heat. Fry the schnitzel for 3-4 min per side until golden and cooked through (internal temperature 74°C / 165°F). Transfer to a plate.
Dice the onion and slice the mushrooms. In the same pan over medium heat, fry the onion and mushrooms for 3-4 min until softened. Add the tomatoes and mustard, stirring to combine. Return the schnitzel to the pan, cover with a lid, and simmer for 10 min.
Remove the schnitzel from the pan. Stir the milk into the sauce and simmer for 2 min. Season the sauce with salt, pepper, and parsley. Serve the schnitzel with the sauce alongside pasta or rice.