Making substitutions in baking is more complicated than it is in cooking. Some ingredients play an important role in the chemistry of a batter -- and you can't change them without making serious adjustments. The good news is that this isn't usually the case with pure flavoring ingredients, such as bourbon or rum. If a brown-butter cake or calls for one, you can substitute the other without difficulty.
Brown Butter in Baking
Butter is primarily considered a fat, but that's only partly true. Whole butter is usually about 80 percent butterfat, with the remaining 20 percent divided between water and milk solids. If you melt the butter over gentle heat, the water evaporates and the milk solids eventually brown. This gives the butter a distinctively nutty flavor -- the French call it "beurre noisette," or hazelnut butter -- that's useful in many dishes such as sole Meuniere. In baking, the nuttiness of brown butter complements other flavorings such as vanilla or bourbon.
Brown Butter and Bourbon
Brown butter and bourbon are often combined in baking, especially in areas where bourbon is the traditional spirit. Ninety percent of all Bourbon produced originates in Kentucky, according to 2012 information provided on the Citiview Louisville website. True bourbon follows a specific distilling and aging process, giving it a distinctive flavor. Its sweetness and hints of woodsmoke and caramel provide an agreeable complement to the richness of the browned butter, each flavor deepening and accentuating the other.
Brown Butter and Rum
If you're out of bourbon but have a flavorful rum on hand, it's one of the better substitutions. Rum's flavor is very different from bourbon's, with its hints of spice and molasses, but it's an equally good complement for the brown butter in your cake recipe. That's especially true if your cake includes warm spices such as cinnamon and allspice, which have a special affinity for rum. Your cake won't taste the same as it did with bourbon, but it the flavors will still complement each other and the end result will be enjoyable.
A variety of other substitutions can work in the same cake, each bringing its own distinctive character. Sour mash, Tennessee whiskey and other bourbon-like spirits are the closest in flavor, though they're typically milder than a true bourbon. Blended whiskeys and Canadian whiskey are milder as well, with understated flavors that would leave the starring role to the brown butter. The peaty flavors of Scotch and Irish whiskey stand out in most recipes, which is good if you like their flavors. You can also use other spirits such as brandy and applejack. If you have no suitable spirits available, add a vanilla bean or vanilla bean paste to your recipe to provide a similarly insistent flavor.