In a small saucepan, bring the water to a gentle simmer over medium heat. Remove from the heat, add the chai tea bags, and steep for 5 minutes.

While the tea steeps, whisk together the milk, pumpkin purée, maple syrup, vanilla extract, pumpkin pie spice, cinnamon, and salt in a separate small saucepan or microwave-safe container.

Warm the pumpkin milk mixture over low heat until steaming, but do not boil. Stir until smooth and well combined, then remove from the heat.

Discard the tea bags and stir the warm pumpkin milk mixture into the brewed chai. Taste and adjust sweetness if desired.

To make the cold foam, combine the cold milk or cream, pumpkin purée, maple syrup, and vanilla in a jar, tall cup, or frother. Froth until thick and foamy.

Fill two glasses with ice and pour the pumpkin chai tea over the ice.

Spoon the cold foam over each glass and finish with a light sprinkle of pumpkin pie spice or cinnamon. Serve immediately.