If the beef slices are thicker than about 1/4 inch, place each between plastic wrap and pound gently with a meat mallet to about 1/8–1/4 inch thickness. Trim excess fat and season both sides lightly with 1 tsp kosher salt and 1/2 tsp black pepper (from ingredient list).

Set up breading station

Arrange three shallow bowls: 1) flour (1 cup) seasoned with 1/2 tsp salt and 1/4 tsp black pepper, 2) whisk together eggs (3) with 3 tbs milk and 1 tbs water until homogenous, 3) breadcrumbs mixed with chopped parsley (2 tbs), garlic powder (1 tsp), paprika (1 tsp) and a pinch of salt.

Bread the beef

Working one piece at a time, dredge a beef slice in seasoned flour, shake off excess, dip into the egg mixture allowing excess to drip, then press firmly into the breadcrumb mixture to coat both sides. Place breaded cutlets on a rack or plate; let rest 5–10 minutes to set the crust.

Fry the cutlets

Heat a large skillet over medium-high heat and add vegetable oil (about 1 cup) and butter (2 tbs) if using. When oil is shimmering (350°F / a small piece of breadcrumb sizzles immediately), fry 2 cutlets at a time without crowding: about 2–3 minutes per side until golden brown and internal temperature reaches 145°F (beef) or crust is deep golden. Transfer to a paper-towel–lined rack to drain and keep warm in a 200°F oven while you finish remaining cutlets.

For the Potato Purée (mashed potatoes)

Place peeled and halved potatoes in a pot, cover with cold water by 1 inch, add 1 tsp salt, and bring to a boil. Reduce to a simmer and cook until tender when pierced, about 15–20 minutes depending on size.

Drain potatoes well and return to hot pot for 1 minute to evaporate residual moisture. Mash or pass through a ricer, then stir in 2 tbs butter and 3 tbs milk until smooth and creamy. Season to taste with 1/2 tsp black pepper and more salt if needed. Keep warm until plating.

For the Simple Tomato Salad (topping)

Combine diced tomatoes (2 cups), chopped red onion (1/4 cup), and 2 tbs chopped parsley in a bowl. Whisk together olive oil (2 tbs) and red wine vinegar (1 tbs) with 1/2 tsp salt and 1/4 tsp black pepper; toss with tomato mixture. Let sit 5–10 minutes to marry flavors.

Plating and finishing

Divide the potato purée among 4 plates, spreading it slightly to make a bed. Place one hot milanesa cutlet on top of each bed of potatoes.

Spoon a generous couple of tablespoons of the tomato salad over each cutlet. Garnish with chopped parsley and a lemon wedge on the side. Serve immediately, squeezing lemon over the milanesa just before eating.