Poet Will Percy provided this recipe for the Mint Julep in his autobiography, Lanterns on the Levee:
First you needed excellent bourbon whisky; rye or Scotch would not do at all. Then you put half an inch of sugar in the bottom of the glass and merely dampened it with water. Next, very quickly—and here was the trick in the procedure—you crushed your ice, actually powdered it, preferably in a towel with a wooden mallet, so quickly that it remained dry, and, slipping two sprigs of fresh mint against the inside of the glass, you crammed the ice in right to the brim, packing it with your hand. Last you filled the glass, which apparently had no room left for anything else, with bourbon, the older the better, and grated a bit of nutmeg on the top.
It sounds like his cousin and ward, Walker, followed a similar, but not identical, method:
Southern writer Walker Percy insisted that a good julep should hold at least 5 ounces of bourbon: 5 ounces bourbon/Several sprigs fresh spearmint/4 to 5 tablespoons superfine sugar/Crushed ice . . . Into a silver julep cup, a highball glass, or a Mason jar, press 2 or 3 tablespoons of superfine sugar together with a very small quantity of water, just enough to make a sugary paste. Add a layer of fresh spearmint leaves. Press them gently with a muddler or wooden spoon, but do not smash them. Pile on a layer of fresh finely crushed ice. Mr. Percy prefers that you reduce the ice to powder by wrapping it in a dry towel and banging it with a wooden mallet. To that layer, add a fine sprinkling of sugar and a few more mint leaves that you have spanked, but not crushed, by clapping them loudly between your hands. Amy Stewart, The Drunken Botanist.
A few simple Google searches reveal that there is also a thing known as a "gin julep" and some heretics actually make the mint julep with vodka. I might have to try it next spring when my mint pops back up (which is assuredly will, even though I eradicated 80% of it last fall to make room for my fall kale planting).