Preheat oven to 425°F. Line a baking sheet with parchment paper.
Toss potato wedges with olive oil, oregano, salt, and pepper. Spread evenly on baking sheet and bake for 25-30 minutes, flipping halfway.
In a small bowl, whisk together mayo, vinegar, water, mustard, garlic, and a pinch of salt and pepper for the dressing.
Season steaks with salt and pepper. Heat a skillet over medium-high heat and cook steaks for 3-4 minutes per side, or to desired doneness. Let rest.
In a mixing bowl, toss arugula with the dressing and top with Parmesan.
Slice steak and serve with oven fries and salad. Garnish with parsley if using.