For the infused Gin, combine the gin, garam masala, and cinnamon stick in a seal-able jar and shake until contents are incorporated. Let sit and agitate about 3 times over a 24 hour period. After settling, there should be quite a bit of spice mixture still sitting in the bottom of the jar (it does not fully dissolve). After 24 hours, strain your infused gin through a coffee filter.
To make the garam masala cocktail add the gin, fresh mango juice, lime, and mint together in a cocktail shaker with ice. Shake until well incorporated. Serve without ice in a shallow glass and garnish with lime and mint. Enjoy!