I melted the butter over low heat, then ramped it up to just begin to brown the butter, then lowered the heat again after adding the eggs.

Wow amazing how did you actually pull that off?

Temperature modulation. See my comment.

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I mean yeah I seen that I’m just wondering how someone ( who is not Gordon Ramsey)could mail it like this.

Pretty sure I saw this on Master Chef and the judges were gushing over it

is frying an egg specifically in brown butter supposed to be hard???

Looks great, a lot like the fried eggs I make. I sometimes use butter, but often duck fat, olive oil or coconut.

The best thing to do is to get the oil as hot as possible before adding in the egg. Put a splash screen (not a lid) and the let it rest to get a good crispy layer before flipping it. You could have let it rest a bit longer for that deep rich golden brown but that's just my preference.

Here's something I recommend you try as well, when there's about 30-60 seconds left to the cook, slowly drizzle in 1tsp-1tbsp soy sauce, tamari, or miso paste diluted in water on the eggs and let that reduce a bit and glaze the egg on both sides, serve with a few drops of sesame oil per egg.

Hoisin sauce can also be added at the soy sauce step for a variation.

Easy to learn hard to master, because there is infinite room for improvement.

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Pull what off?

I was just joking