In a small saucepan, bring the water to a gentle simmer. Add the cinnamon, cardamom, ginger, cloves, and nutmeg. Stir and let simmer for 2 minutes to release the flavors.
Add the ground coffee directly into the simmering spiced water. Stir, turn off the heat, cover, and then let it steep for 4-5 minutes.
Strain the brewed coffee through a fine mesh sieve or coffee filter into a mug. Stir in the maple syrup (or honey) and vanilla extract.
Warm the milk in a small saucepan over medium heat until hot but not boiling. Froth with a whisk or handheld frother.
Pour the frothy milk over the chai-spiced coffee and stir gently. Optionally, top with a sprinkle of cinnamon or a dollop of whipped cream.