With a vegetable peeler or a sharp knife, pare a 2-inch strip of peel (yellow part only) from the lemon, then cut into long, thin shreds. Cut lemon in half and rub 1 cut side on the rim of a glass (10 to 12 oz.) to moisten; save lemon for other uses. Pour 2 teaspoons sugar on a small plate and dip moist glass rim in it to coat evenly, then pour sugar into glass.
Add 4 mint sprigs to glass. With a wood spoon, crush mint sprigs with sugar to bruise the leaves and release the herb's flavor. Fill glass with ice. Add bourbon, then fill to rim with club soda. Let stand until glass is frosty, about 2 minutes. Garnish with lemon peel and remaining mint sprig. Sip julep through a straw, adding more sugar to taste.