I’m a bit late to the game, but here are a few more ideas. I am kind of a potato nut and make them in a lot of ways.
I saw gratin mentioned above. This is my favorite recipe: https://www.seriouseats.com/recipes/2017/11/classic-potato-gratin-recipe.html
What about a frittata with potatoes or a Spanish Tortilla? (And what about patatas bravas?)
This weekend I made “Polpettone” from the Liguria area. It is not a meatloaf but a potato pie with green beans and potatoes. It would be good with a poached egg on top. Here is a recipe in English. https://www.asmallkitcheningenoa.com/polpettone-potatoes-and-green-beans-tart/?fbclid=IwAR1aea4iWmHx_gYIrPim5btaHTdZjy3vuIbevGuKBGaaTYZLTNgq4li9PaU
In Italy they also make “Gatto’ di Patate” (Really just gateau!) It’s also a potato pie with cheese – can be anything from mozzarella to smoked scamorza - butter, milk and eggs. Also ham, pancetta or salami. Baked with bread crumbs on top. I’m afraid I don’t have a recipe in English, but this one looks pretty close: https://www.christinascucina.com/potato-ham-and-mozzarella-bake/
You can also look up pizza di patate (the Pugliese version) and you’ll find other variations of the same concept.
Speaking of pizza, sliced potatoes and rosemary are delicious on white pizza! With or without cheese. Usually without.
Colcannon is another favorite around here. The Irish mash with cabbage, like this one: https://www.bonappetit.com/recipe/colcannon
Be sure to have awesome butter for this one to melt on it. 😊
Speaking of cabbage and potatoes, Pizzoccheri is another dish from the Valtellina area. It is buckwheat pasta ribbons made with potatoes, onion, cabbage and sometimes also a green leaf vegetable, with a really strong cheese called Casera or Bitto, but maybe something like Fontina would work, and butter here too. This is a very stick to your ribs dish meant for cold weather!
There are other versions of pasta with potatoes around too, but I don’t like it so can’t recommend any.
But I do love potato-filled ravioli, called Tortelli Mugellani. They are like giant tortellini usually served with meat sauce.
I sometimes make potatoes and peppers. You start onions and peppers in a pan and then add potatoes and cook through, maybe getting them crunchy on the bottom. I’ve seen people do this in the oven too.
I also love roasted potatoes, and will roast a million different ways, certainly not as creative/delicious as Shains, but Tuscan style would be rosemary, sage, garlic with the skin on, and sometimes fennel, especially if served with duck.
There is also octopus and potato salad, or oven baked octopus with potatoes, olives, and tomato.
Twice-baked potato boats (The one where you bake them, scoop out, mix with cheese and sour cream etc and then bake again?) Fried potato croquettes? Tater Tots? Potato bread rolls? (My husband uses potato in his Focaccia Pugliese.) Samosas? Classic, Italian or German Potato salad?
Sorry, I went a little overboard. 😜