Preheat your oven to 350°F (175°C). Season both sides of the beef generously with salt and pepper.

Heat vegetable oil in a large skillet over medium-high heat until shimmering. Brown the beef for 2-3 minutes per side until golden. Remove to a plate and set aside.

Reduce heat to medium and add sliced onions to the same skillet. Cook for 5 minutes, stirring occasionally, until soft and translucent. Add minced garlic and cook for 1 minute until fragrant.

Sprinkle flour over the onion mixture and stir constantly for 2 minutes to create a roux. Gradually add milk and beef broth while whisking continuously until the sauce thickens enough to coat the back of a spoon. Remove from heat.

Layer half of the sliced potatoes in a 9x13-inch casserole dish, slightly overlapping them. Pour half of the onion sauce over the potatoes and sprinkle with half of the shredded cheese.

Repeat layering with remaining potatoes, sauce, and cheese. Sprinkle paprika evenly over the top.

Place browned beef on top of the casserole, pressing gently into the layers. Cover tightly with aluminum foil and bake for 1 hour.

Remove foil and bake for an additional 15-20 minutes until beef is fork-tender and potatoes are tender with golden brown edges.

Let the casserole rest for 10 minutes before serving. Garnish with freshly chopped parsley.