Lightly grease a 9x13 casserole dish and set aside. Preheat oven to 350 degrees Fahrenheit.
Peel potatoes, rinse, and slice to ⅛" thickness. I recommend using a mandoline slicer if you have one available.
In a saucepan over medium heat, add butter. Once melted, add onions and cook until they begin to brown and turn translucent, about 4-5 minutes. Add garlic and cook an additional 30 seconds. Add flour and stir to coat and create a paste. Cook for one minute.
Whisk in broth and milk. Continue whisking until no lumps remain. Cook sauce for another 3-4 minutes or until thickened slightly. Remove from heat. Add salt, pepper, and dill, stirring to incorporate.
In your 9x13 pan, arrange about ¼ of sliced potatoes in the bottom of the dish, overlapping slightly. Pour ¼ of sauce over potatoes. Repeat 3x more for a total of four layers of potatoes and four layers of sauce.
Cover casserole with foil and bake for 45 minutes. Uncover and bake an additional 15-20 minutes, or until potatoes can easily be pierced through with a fork in the center of the casserole. The thicker your potatoes are sliced, the longer it will take for them to cook through.
Dried dill can be substituted with dried thyme for a more traditional flavor. I like to use dill in the spring (for holidays like Easter), and thyme in the fall/winter (for Thanksgiving or Christmas).
Dried dill can be substituted with fresh dill at a 1:3 ratio. For every ½ teaspoon of dried dill called for, use 1 ½ teaspoons of fresh dill.
Want to add cheese? - Sprinkle 1 cup of shredded cheese after your second layer of sauce (in the middle of your casserole layers), and then sprinkle the top of your casserole with another 1 cup of shredded cheese before baking. Recommended cheeses: cheddar, monterey jack, gruyere, or parmesan.