How to brown butter properly.
Make sure that you are using a stainless-steel skillet so that you can visually see the butter as it browns. Make sure that you are using unsalted butter, it foams less than salted butter. You want to cook the butter gently to evaporate the water and then increase the heat so the milk proteins floating on the top sink to the bottom of the pan. This will develop a golden brown color and a nutty flavor. Once the butter is browned scrape out of the pan making sure to get all of the flavorful brown milk solids out. You must watch this procedure very closely because it takes just a second for the butter to quickly burn and then you have to start over. If the butter is just mildly burned you can try and strain it through a coffee filter to get all those burnt bits out. Then taste to see if it tastes burnt. If not, you could use it. My advice is if you burn it start over.