Fill a tall glass with ice cubes and set it aside while you prepare the other components. This chills the glass so your finished drink stays cold longer.

Pour 1/2 ounce of simple syrup into the bottom of a fresh glass.

Take half a lime and cut it into 2-3 wedges, leaving the skin attached so you can squeeze the juice directly into the drink.

Place the mint leaves and lime wedges into the glass with the simple syrup, then gently press them together with a muddler or the back of a spoon using 4-5 light pressure strokes. Don't crush the mint aggressively.

Squeeze the remaining lime wedges directly over the muddled mixture to extract all the juice.

Pour the entire muddled mixture, along with all the liquid and mint leaves, into your prepared glass filled with ice.

Fill the glass with 4-6 ounces of cold club soda. Add the soda slowly so it doesn't overflow.

Give the drink a gentle stir with a bar spoon to combine all the flavors evenly, then take a sip and adjust if needed.

Place a sprig of fresh mint on top of the ice and drop a lime wheel on the rim for garnish. Serve immediately while the drink is coldest and the carbonation is most lively.