Make the beurre noisette: put the butter in a medium saucepan (not too small, you want a reasonably large surface area), place over medium heat, and watch, swirling the pan every now and then to ensure an even heat distribution. First, the butter will melt. Then, bubbles will form at the surface as the butter simmers and its water content evaporates. The butter “sings” during that phase, emitting a pleasant chirping sound.
A few minutes later, the bubbles will get smaller, and the pitch of the chirping sound will get higher, then stop. At this point, the smell of the butter will change and become distinctly hazelnutty — you can’t miss it, it’s the best thing you’ve ever smelled, and the ambient scent of cr?peries in Brittany — as its color becomes bronze and little flecks of butter solids caramelize and turn golden brown at the bottom of the pan.
(Don’t let it cook beyond this stage, or the butter solids will get too dark, eventually burning and turning black and bitter and carcinogenic, in which case you’ll have to strain the brown butter through a fine sieve and sacrifice the flavorful caramelized bits.)