Place cinnamon and sugar in a shallow bowl. Dip rim of a glass into a shallow plate with 1 Tbsp. rum; dip in cinnamon-sugar to coat.
Combine Butternut Squash Base, remaining 3 Tbsp. rum, orange liqueur, and next 3 ingredients in a cocktail shaker filled with ice. Squeeze juice from lemon wedge into shaker. Stir, then shake until well chilled. Strain into rimmed glass.