Place the whole cloves and green cardamom pods in a mortar and pestle and crush them thoroughly. Mix in the ground cinnamon and ground ginger. If using whole cinnamon sticks and fresh ginger root, crush or chop them along with the cloves and cardamom.
Toast the crushed spice mixture in a dry pan on the stove over low heat for 3 to 4 minutes, stirring occasionally.
Transfer the toasted spices to a pot with the water. Bring to a boil, reduce heat, and simmer for 15 minutes. Bring back to a boil, then immediately remove from heat.
Add 5 Assam tea bags and steep for 4 to 5 minutes only. Do not oversteep.
Strain the mixture through a fine-mesh sieve into a container to yield the chai concentrate. Let it cool completely.
In a mug or small pitcher, combine almond milk, vanilla syrup, and cinnamon powder. Froth with an electric hand frother for 15 to 30 seconds until rich and creamy.
Add ice cubes to a glass, pour in equal parts chai concentrate and frothed almond milk, stir in sweetener, and serve.