I like sharp, classic, bracing cocktails most of the time. But I always have a mint julep on Derby Day and occasionally on a hot day in summer. My version is mostly traditional, just culled together from several methods I've tried.
You can use 2 tbs simple syrup instead of the brown sugar and water, but I prefer mixing it on the spot, and also in separate glasses for each person instead of all in one container.
1 tbs brown sugar, packed in the spoon
2 tbs water
3 sprigs spearmint; if you can get Kentucky Colonel mint, use that because it's awesome
3 oz good bourbon
1 tray of ice, chopped up or crushed, depending on your equipment and patience
Put the sugar and water in a double rocks or large wine glass or the like, and add two mint sprigs that each have several leaves on them. Muddle with a wooden spoon or stir vigorously for at least a minute. Set it aside.
Chop or crush your ice, or if yours already came that way, just let the mint syrup sit for about five minutes, add half the ice to the glass, stir vigorously, add the other half, then pour the bourbon over it and stir lots more. Garnish with the third mint sprig.
Don't add anything else. If you do, you've made some other kind of drink. Which is fine, but not at all the point.
If you actually have a silver cup, sure, use that. But if you're using a silver cup for a mint julep, you don't need anyone to tell you how to make one. :-)