Combine heavy cream and cinnamon stick in a small saucepan. Bring to a boil; reduce heat, cover, and simmer for 10 minutes. Remove pan from heat; discard cinnamon stick. Add 3 tablespoons maple syrup and cardamom.
Bring water to a boil in a large saucepan; add oats and salt. Cook and stir for 5 minutes. Remove from heat, add cream mixture, 2 tablespoons maple syrup, and brown sugar; stir to combine. Cover and let stand for 2 minutes.
Set oven rack 4 to 6 inches from the heat source and preheat the oven's broiler. Grease seven 6-ounce ramekins.
Divide blueberries equally among the ramekins. Spoon oatmeal mixture on top. Sprinkle white sugar over oatmeal. Place filled ramekins on a rimmed baking sheet.
Broil in the preheated oven until sugar is melted, 7 to 9 minutes.
