1. To make the brown butter bourbon, melt the butter in a skillet or wide saucepan over medium heat. Continue to cook the butter; it’ll sizzle and pop as it cooks, which is the water cooking off.
2. As the butter cooks, tilt the pan to avoid burning in spots. When the butter quiets down and has turned a nice amber brown color, and smells deliciously nutty, remove from heat and let cool until tepid.
3. Pour the bourbon (or rye) into a jar, add the brown butter, close the jar and shake a few times to mix the butter with the bourbon. Refrigerate the bourbon for three days.
4. After three days, place the jar of bourbon in a saucepan with an inch or two of water in it. Very gently start to warm the bourbon over low heat in the water bath. As soon as the hard disk of butter on top is removable, lift it out (reserve it for another use, see Note at end of recipe). Line a funnel with a few layers of cheesecloth, a paper towel or coffee filter, set over a clean jar. Strain the bourbon into the jar. Chill the bourbon until ready to use.
5. To make the Old Fashioned cocktail, use a muddler or back of a spoon to mix the bitters with the sugar in a squat cocktail glass, until the sugar is dissolved. Add the bourbon and a large ice cube and stir for 15 seconds until the cocktail is well-chilled. Twist a strip of orange zest over the glass, so the oils spray into the drink, drop the zest into the glass, and serve.