Sterilize the jars and cooking utensils you will be using and gather your ingredients.
Peel the mangoes and cut into large chunks. Add to the jar.
To prep your lime peels, if your citrus is not organic, boil the limes in hot water for 3 minutes. Then wash them with mild soap and wipe dry to remove any remaining preservatives from the surface. If using organic limes, skip this step. Make 2 to 3 strips of lime peel (around about a half of a lime). Peel off the very top skin leaving the pith behind. If you need to, using a sharp knife, safely and gently remove as much of the white peel, or pith, as you can. Add to the jar.
In a small pan over medium-high heat, toast the star anise (see Notes above on brands of star anise) for a minute or two until fragrant. Add to the jar and pour the rum to cover all the ingredients by 1/2 an inch.
Infusing
Allow the mixture to infuse in a dark place at room temperature for 2 days. Taste and see if the mango and star anise flavors are strong enough, keeping in mind that it has not been sweetened yet! If the star anise flavor is strong enough but not the mango, with a very clean spoon, fish out the star anise and allow the infusion to rest another day. Taste daily until you think your liqueur is ready.
Strain the liquor through cheesecloth into a decanter or covered jar.
Sweeten with Simple Syrup
Make a 1:1 sugar to water solution using white (granulated) sugar. In a small pan over high heat, mix together 1/4 cup sugar and 1/4 cup water. Stir to dissolve the sugar; remove from the heat, and allow it to cool. Simple syrup can be made with superfine sugar without heat, stirring continuously until the sugar is dissolved.
Starting with 3 tablespoons of simple syrup, sweeten the liqueur to your taste.
Serve! Store at room temperature in a dark place for up to six months.
A Simple 3-ingredient Mango Liqueur Cocktail
Mix everything together and serve over ice. Taste and adjust the lime/lemon juice and amount of club soda. If you need sweetness add more simple syrup or maple syrup.
Notes
Light or white rum suggestion if you don't have a favorite:
Havana Club, Appleton white rum, Flor de Caña
For pure mango flavor, steep in vodka, and skip the spices. The mango infusion is very good all on its own.
Get a good quality star anise. The Swagat brand, while great for curries, did not make a great liqueur. I can vouch for the Penzeys and Frontier Co-op brands.
If you are experimenting or afraid to make a commitment to almost a whole bottle of rum, make a 1/2 batch mango liqueur.