Make ginger sugar syrup by putting sugar and water into a small saucepan over a medium heat. Once the sugar has dissolved add the ginger pieces. When liquid starts to boil leave it for 2 minutes, then take it off the stove top. Set aside to cool.
Place lime wedges and ginger sugar syrup into glass part of Boston shaker. Muddle for about one minute using your muddler. Next bruise mint by clapping leaves between palms of hand and place into shaker.
Next add tequila and pineapple juice into shaker and fill with ice. Place metal tin on top of shaker and shake vigorously for about 30 seconds. Then dump all ingredients into highball glass or something similar. Garnish with a lime wedge and a mint sprig.
Drink