Preheat your oven to 350°F. While it heats, scrub the potatoes and slice them into 1/8-inch thick rounds—I like to use a mandoline for consistent thickness, which helps them cook evenly. Dice the small onion and mince the garlic. Measure out all your seasonings (paprika, salt-free seasoning, mustard, poultry seasoning, thyme, and black pepper) into a small bowl so they're ready to add quickly to the sauce.
Melt the unsalted butter in a medium saucepan over medium heat. Add the diced onion and cook for 3-4 minutes, stirring occasionally, until softened and slightly translucent. Add the minced garlic and cook for another 1-2 minutes until fragrant. Sprinkle the flour over the mixture and stir constantly for 1-2 minutes to create a roux—this removes the raw flour taste and helps thicken the sauce.
Lower the heat to medium-low and slowly whisk in the room-temperature milk and chicken broth, stirring constantly to prevent lumps from forming. Keep whisking until the sauce thickens enough to coat the back of a spoon, about 3-5 minutes. Add all the seasonings from your prepared mixture and stir well to combine. Increase heat to medium and bring the sauce to a gentle boil while stirring constantly for 1 minute—this helps the flavors meld and ensures the sauce is properly thickened. I like to taste a small spoon of sauce at this point and adjust seasonings if needed, since we're using low-sodium ingredients.
Pour a thin layer of the sauce from Step 3 onto the bottom of a 9x13-inch baking dish. Arrange a layer of sliced potatoes over the sauce, then pour more sauce over them. Repeat this layering process until all potatoes and sauce are used, finishing with a layer of sauce on top to prevent the top potatoes from drying out during baking.
Cover the baking dish tightly with foil and bake for 45 minutes at 350°F. Remove the foil and bake for an additional 35-45 minutes until the potatoes are tender when pierced with a fork and the top is lightly golden. If you want an extra-creamy top layer, broil for 2-3 minutes until golden brown—watch carefully as broilers vary in intensity. Let the casserole rest for 15 minutes before serving; this allows the sauce to set slightly and makes it easier to serve clean portions.