An optional step for an even deeper cardamom flavor is to dry-toast the cardamom seeds over low heat for 3-5 minutes.
Heat the water in a metal-bottom pan until just simmering.
Meanwhile, grind your cardamom seeds with a mortar and mestle or lightly pulse them in a spice grinder, until coarsely ground but not nearly as fine as ground cardamom from the store.
Then once your water is simmering, pour in your sweetener and stir everything together until the sweetener has dissolved, and bring everything back to a low boil, then add the cardamom seeds.
Heat the cardamom syrup mixture on low for 10 minutes (set a timer), never letting it get above a simmer, stirring occasionally.
When your timer goes off, remove the mixture from the heat and let it sit on a cool burner for 15-20 more minutes (to infuse further).
Then strain the mixture and preserve your cardamom syrup in a closed container in the fridge for up to 10 days or in the freezer for up to 6 months.