Preheat your oven to 375°F. Lightly coat a 9×13-inch glass or ceramic baking dish with non-stick cooking spray and set it aside.
Heat a large skillet over medium-high heat. Add the lean ground beef and diced yellow onion. Cook for 5 to 6 minutes, breaking the meat up with a firm wooden spoon, until the beef is fully browned and the onions are soft.
Add the minced garlic, ½ teaspoon of the salt, the black pepper, and the paprika to the skillet. Cook for 1 more minute until fragrant, then drain away any heavy pooling grease and remove the pan from the heat.
In a medium mixing bowl, combine the condensed cream of mushroom soup, sour cream, whole milk, the remaining ½ teaspoon of salt, and exactly 1 ½ cups of the shredded cheddar cheese. Whisk firmly until the elements form a thick, uniform sauce baseline.
Arrange half of your thin potato slices in an overlapping layer across the entire bottom of the prepared baking dish.
Spread half of the cooked ground beef mixture evenly over the potato layer, then spoon half of the creamy cheese sauce baseline over the meat, smoothing it out with a spatula.
Repeat the layers one more time: arrange the remaining potato slices, top with the rest of the ground beef, and spread the remaining cheese sauce uniformly over the surface.
Cover the baking dish tightly with aluminum foil. This step is critical because it traps the interior steam needed to soften the potato matrix.
Bake at 375°F for 40 to 45 minutes. Carefully remove the foil and poke the center with a fork to ensure the potatoes are completely fork-tender.
Scatter the remaining 1 cup of shredded cheddar cheese evenly across the top of the casserole. Return the dish to the oven uncovered for an additional 8 to 10 minutes, or until the cheese matrix is entirely melted, bubbly, and lightly golden around the edges.
Remove the casserole from the oven and let it stand flat on a cooling rack for 10 minutes. This resting window allows the rich sauce to tighten slightly so it scoops beautifully. Garnish with fresh parsley and serve hot.