Place cubed potatoes in a large pot, cover with cold water by 1 inch, add 1 tablespoon of salt, and bring to a boil. Cook on medium-high for 8–10 minutes until fork-tender but still holding their shape, then drain thoroughly and let steam dry for 2–3 minutes.
Return drained potatoes to the pot and use a potato masher to roughly mash about half of them, leaving the rest in chunks for that signature "muddy" texture.
Lay bacon strips in a cold heavy-bottomed skillet, turn heat to medium, and cook 12–15 minutes, flipping occasionally, until crispy. Drain on paper towels, cool, then crumble into bite-sized pieces, reserving ¼ cup for topping.
In a large bowl, whisk together sour cream, milk, and melted butter until smooth, then stir in ranch seasoning, minced garlic, salt, pepper, and paprika. Fold in the 1½ cups cheddar, all the Monterey Jack, and most of the crumbled bacon.
Preheat oven to 350°F (175°C) and generously grease a 9x13 inch baking dish with cooking spray or butter, including the sides and corners.
Fold the potatoes into the creamy cheese mixture until every piece is coated, then spread evenly into the prepared baking dish, pressing down gently to eliminate air pockets.
Sprinkle the reserved ½ cup of cheddar evenly over the top, then scatter the reserved ¼ cup of crumbled bacon over the cheese.
Cover the dish tightly with aluminum foil (tented so it doesn't touch the cheese) and bake for 45 minutes.
Remove the foil and bake an additional 25–30 minutes until the top is golden brown, the cheese is lightly crispy, and the edges are bubbling.
Let the casserole rest for 10 minutes to set up, then top with sliced green onions and serve immediately with a large spoon, scooping all the way to the bottom to get every layer.