If you are using the packet rösti in my experience you need to leave it in the pan for way way longer than the time on the packet without actually disturbing it.
Then you can flip it fairly easily and brown the other side.
if it is not sticking to the pan, then you just need to flip it so it turns in one go. work on the flipping technique or slide off the pan onto a plate put pan over it and flip it back on the pan.
After 10 years I am still trying to figure out on how to get it out of the pan in one piece. Last time I was so frustrated that I put it in the oven instead LOL
Exactly this, I cook rösti for wayyyyy longer than it says on the package. I also use roasting oil in place of butter. Also, before trying to flip it out of the pan use a spatula to make sure it is loose from the bottom. If the rösti sides around when you give the pan a bit of a jiggle you're good to go.
Pro advice : If you master first how to do a Spanish tortilla, rösti will be easy.
Going through your text again, your only problem is that the rösti sticks to the pan?
what kind of pan are you using, I guess it is not non-sticking?
a. use a non-sticking pan
b. tell us what kind of pan are you using, so maybe we can guess the right technique, but basically, you need to dry and brown the lower side of rösti without burning it. So, kind of the right amount of heat for the size of the pan / thickness of rösti.
I've had good results with my seasoned cast iron pans, not so much with other pans on the stove unless I use waaaaaaay more butter than my arteries can take.
But because I have an electric stove, I can't use the cast iron on that. So I do it in the oven, in the cast iron skillet. Once golden brown on top, take out and flip, then keep going until the other side is nicely golden brown too.
I use my smallest cast iron skillets, easier to flip.
On the beginning mixid up scrap the bottom and wen it is all trout golden brown , ad butter if needed , let it stay and a wile and then flipped on a platte My wife is Irish and she learned it ,now I am not allowed in the kitchen anymore
with a lid on, you are kind of boiling, stewing it, as it keeps all moisture in
You want your packet open first. When the pan it at optimum high heat, woosh add the mixture
you can give pan a shake around for the mixture to settle
you can turn the pan down depending what kind of pan you have
what heat is trial and error depending on the pan, usually we have it kind of high to toast both sides, we electric heating, so that varies what you use.
The stove is not induction, maybe that's the problem. But so many of my signature cast iron dishes, those that reliably turned out perfect on my gas stove, end up a mess on electric.
So I use my cast iron either in the oven or on the burner on the outside grill, but not the stove.