How to cook salmon (recipe calling for pan frying)

I'd like to make this recipe:
https://www.nigella.com/recipes/mirin-glazed-salmon

But I have kind of unevenly thick portions of salmon. The last time I made it, the sauce and the outside of the salmon began to burn because it was taking so long for the salmon to cook in the pan. So my questions are:

1) Obviously if my sauce burned, I probably added the sauce too early. But my issue is that the outside of the salmon also starts burning if I leave it in the pan too long (trying to cook the salmon). Should I par-bake the salmon in the oven? What would that look like? 350(F) for 8 mins?
2) Side question: what kind of pan do you use? I was trying to use green pans, but those aren't really nonstick. I suppose I should invest in a carbon steel or cast iron pan right?

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