Step 1: Prepare the Potatoes
Preheat the oven to 375°F (190°C).
Grease a baking dish with a bit of olive oil to prevent sticking.
Slice the potatoes thinly and layer them on the bottom of the baking dish. Drizzle with olive oil, and season with salt and pepper. Set aside.
Step 2: Cook the Meat and Vegetables
In a large skillet, heat a tablespoon of olive oil over medium heat.
Add the chopped onions and sauté until softened, about 5 minutes. Then, add the minced garlic and cook for an additional minute.
Add the ground beef to the skillet, breaking it up with a spoon as it cooks. Cook until browned, around 7-10 minutes.
Add the chopped celery and mushrooms to the beef mixture, cooking until the vegetables soften, about 5 more minutes.
Season the filling with 1 tsp of salt, 2/3 tsp of black pepper, and 1 tsp of paprika. Mix well, and cook until everything is fully combined and fragrant.
Remove the skillet from the heat.
Step 3: Assemble the Pie
Spread half of the cooked meat mixture evenly over the layer of potatoes in the baking dish.
Pour half of the beaten eggs over the meat mixture, allowing it to settle among the ingredients.
Add another layer of thinly sliced potatoes on top, and season lightly with salt and pepper.
Spread the remaining meat mixture over the potato layer, and pour the remaining beaten eggs over the top.