Helen was a friend of my parents, the kind of friend who would show up with food & sympathy for sad occasions or food & happiness for joyous occasions. One dish she often brought for any occasion was her Cheesy Potatoes. Her original recipe called for 4x every ingredient, put into a LARGE roaster and baked for 60-90 minutes. I'm quartering her recipe for the average family. The cheese sauce also makes a delicious baked mac & cheese with 1/2 pound of cooked pasta. Halving the cheese sauce would give you the perfect amount for broccoli & cheese. Thanks, Helen. I remember your love. =^..^=
Earlier in the day, or the night before, cook the potatoes in a pot of water until just done. (I use red-skinned potatoes so I don't have to peel, but if you use regular potatoes, cook them with their skins on, then peel the skins off right before slicing them.) Drain & cool completely. Refrigerate, if cooking them the night before.
When it's time to put the dish together, slice the potatoes into a cooking-sprayed 13 x 9" pan. (This photo shows regular potatoes with their peels removed before slicing into the baking dish.)
To make the cheese sauce, melt the butter in a saucepan over medium heat. Stir in the flour with a whisk. Add the milk & salt and continue stirring constantly. Cook until the sauce is hot and starts to thicken. Remove from heat.
Stir in the shredded cheddar cheese until melted. Slowly add additional milk while stirring, until the cheese sauce is thinned to the desired consistency.
Pour the cheese sauce over the sliced potatoes, covering completely. Using a spoon, lift up potatoes from the bottom so the sauce will run down. (If the cheese sauce is too thick, just pour a little bit of milk over the potatoes and don't worry about it. They'll still turn out fine after baking.)
Bake at 350 degrees F. for around 25 minutes, until the dish is bubbly in the middle and the cheese on the top looks done.