This morning, I feel like I turned a corner in my Sunday morning hash-brown making skills.
For starters, I used a dutch-oven style pan, with a lid. The lid helps keep in the steam, which is important for helping the potatoes get softened up. Add some olive oil, and set the burner to medium heat. I also cooked everything in layers, as opposed to cooking them all mixed up, and this seemed to help a lot.
First thing I did was chop up two onions, and deposit them in the oil to start frying. Previously I just stirred them in with everything else, but leaving them frying in the pan while I cut up the potatoes helped them to caramelize a bit, which helps. When I added the potatoes, I just dumped them on top of the onion layer, and let them there for a while, with the lid on the pan. The downside is that some of the onions on the bottom will burn to the pan. But this is easily fixable. The upside is that those same onions release a bit of sugar into the mix, which definitely helps. They also release a lot of water in the form of steam, which helps cook the potatoes.
Once the potatoes started to soften up, I added some chopped scallions, salt, pepper, and dill, stirred the whole thing up. Cook for a few more minutes with the lid still on, and then it's ready to serve.
If I wanted to add anything to the process, I'd probably add another frying pan, at a higher heat, to brown the potatoes. But that's more to clean up, and it feels like it'd be a better trick to perform on an industrial diner griddle.