Add all of the ingredients to a Julep cup or double Old Fashioned glass.
Fill halfway with crushed or pebble ice, then swizzle to chill.
Pack the glass with more ice, forming a mound at the top.
Garnish with the mint and finely grated lemon zest over the surface of the drink.
*Green tea syrup: In a saucepan, bring 2 cups of water to a boil. Reduce to a simmer, add 4 green tea bags, and simmer for 5 minutes. Remove from heat, discard the tea bags, and stir in 2 cups of sugar until it dissolves. Let the syrup cool; it can be stored in the refrigerator for up to 2 weeks.