Rummy Roman Holiday

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1/2 to 3/4 cup simple syrup (see Cook's Note)

2 cups loosely packed fresh mint leaves, plus more sprigs for garnish 

2 cups amaro, such as Averna

2 cups dark rum 

2 cups sweet vermouth 

1 1/2 cups fresh lemon juice 

1/2 cup fresh orange juice, plus an orange wedge, for garnish 

Club soda, for topping off