Melt 4 tablespoons butter in a large skillet over medium heat. Add 1 large yellow onion, finely diced, and cook until very soft and lightly golden, about 6–8 minutes.

Stir in 3 cloves minced garlic and cook for 30 seconds.

Sprinkle in ⅓ cup all-purpose flour and cook, stirring constantly, for 1–2 minutes to remove the raw flour taste.

Slowly whisk in 2 cups whole milk, 1 cup chicken broth, and ½ cup heavy cream. Bring to a gentle simmer and cook until thickened, about 3–5 minutes.

Stir in 1½ teaspoons kosher salt, ¾ teaspoon black pepper, ½ teaspoon smoked paprika, and ½ teaspoon Dijon mustard. Taste and adjust seasoning.

Lightly butter slow cooker insert. Layer one-third of 3 pounds peeled, sliced Yukon gold potatoes in an even layer across the bottom.

Spoon one-third of sauce over potatoes, then sprinkle with one-third of 1 cup shredded cheddar or gruyere and one-third of ¼ cup grated parmesan.

Repeat layers two more times with remaining potatoes, sauce, and cheese, finishing with remaining sauce and remaining parmesan on top.

Place a double layer of paper towels across the top of slow cooker insert, then cover with lid. Cook on LOW for 5–6 hours or on HIGH for 2½–3 hours, until potatoes are very tender when pierced with a knife.

Remove lid and let rest uncovered for 15 minutes before serving to allow sauce to thicken.

For a golden, browned top: transfer to a baking dish, sprinkle extra cheese over top, and broil for 3–5 minutes until golden and bubbling.