Crush the cardamom pods with the flat edge of a knife. Pry them open and drop the seeds in a spice grinder along with the cardamom husks. Pulse until the seeds are a coarse powder and set aside.
Add the sugar and the water together in a medium saucepan over medium-low heat. Stir until the sugar is completely dissolved.
Add the oranges, cardamom, and thyme and cook for 10 to 15 minutes or until the syrup has become the color of the fruit and the fruit has lost its vibrancy.
Add the vinegar and bring the mixture back to a simmer (about 5 to 8 minutes).
Strain using a fine-meshed sieve covered with one layer of cheesecloth.
Pour into a jar and keep it in the fridge.