In a large, clean skillet heat 2 tbsp butter over medium heat. Add the squash in a single layer. Cook for 5-6 minutes until the squash is browned on one side. Flip and cook for 3-4 minutes more until second side is also browned.
Add 1/2 cup brown sugar, 1/3 cup water, 1 cinnamon stick, and 3 green cardamom pods (if using). Cover and cook on low heat for 10 minutes. The squash is cooked once it gives easily when pierced with a knife.
Discard spices and transfer squash pieces to a plate. Add 1/2 tsp kosher salt and remaining 2 tbsp butter to the liquid in the pan. Stir well to emulsify the butter until a thick, glossy sauce forms.
Serve slices of squash with caramel sauce, candied seeds, and a dollop of sour cream, yogurt, or ice cream.