For best results, use high-quality fresh unsalted butter. Since you'll be reducing the butter by evaporating the water in it, you'd wind up with an inedibly salty butter if you start with the salted kind.
While brown butter is really simple to make, it's also all too easy to ruin it completely because it goes very quickly from lusciously flavorful, rich brown to black and bitter. If you're not used to preparing it, it's a good idea to brown your butter slowly until you get the hang of it.
Use a heavy-bottomed pan, and if you have a light-colored one that will enable you to check the butter color as it cooks, so much the better. Cut the butter into even pieces, about 1-inch thick, and cook over medium heat, stirring occasionally with a wooden spoon or heat-proof rubber spatula. As the water cooks off and the butter melts, the milk solids will drop to the bottom and the proteins will foam at the top.
At this point, when the butterfat is a clear yellow liquid and the milk solids have not yet colored, you have clarified butter. Now the temperature of the butterfat is high enough to brown the milk solids. Keep your eye on the milk solids: as they caramelize and brown, they become more flavorful, but you need to take the pan off the heat before they turn dark. I simmer until the butter is a rich nut-brown. Remember that the butterfat stays hot and will keep cooking the solids even after you remove the pan from the burner, so err on the side of caution. If the pan is still bubbling furiously and browning too much, immediate transfer the brown butter to a heatproof bowl to cool it down.
To strain or not to strain? There is lots of flavor in those browned solids, so it's usually best to leave them as is. In light, more delicate dishes (like my Applesauce with Rosemary and Brown Butter-see the recipe here on the Centropa website), I sometimes pour the brown butter through a very fine strainer to eliminate some of the foam.
If you're not using the butter right away, transfer to a bowl and store, well-wrapped, in the refrigerator.
In addition to stirring it into applesauce, use brown butter for melted butter sauce, either as is or heated with an herb like sage. Make a simple, homey dish of brown butter tossed with egg noodles, and served either plain; mixed with farmer, pot, or cottage cheese; or combined with ground walnuts or poppy seeds and a little sugar. Pour brown butter over cheese, potato, and kasha kreplach and pierogi. For crunch, sauté some challah crumbs in the brown butter and use to top the noodles and kreplach. You can also add lemon juice and capers and serve as a sauce over fish or vegetables.
It's also terrific with other starches: pour over couscous (especially good mixed with dried fruit and nuts), lentils, or stir into kasha varnishkes or mashed potatoes with onions.
Substitute the brown butter for melted butter in recipes for blintzes, crepes, and such; serve as an accompaniment to waffles and pancakes.
For baked goods, like cookies and cakes, where solid butter is called for, transfer the brown butter to a shallow bowl and chill in freezer until just congealed, about 15 minutes. Or if not using right away, chill in a bowl in the refrigerator until congealed. To use in your regular baking recipes, you may need to need to add a bit more liquid (since the water is evaporated out when cooking the brown butter) or adjust cooking time (undercooking slightly), to prevent dryness.