Lightly crush the cardamom pods and ginger.
In a small saucepan, combine 1 cup water with the crushed cardamom pods and ginger. Bring to a boil over medium-high heat.
Add 2 heaping teaspoons of strong black tea leaves and boil for 2 to 3 minutes, until the liquid is very dark.
Stir in 3/4 cup whole milk and 2 1/2 teaspoons of granulated sugar. Bring back to a boil.
Reduce heat to low and simmer gently for 5 to 7 minutes, stirring occasionally.
Strain the chai through a fine-mesh strainer into serving cups, discarding the tea leaves and spices. Serve immediately.