Place the milk, freshly grated ginger, cinnamon, and cloves (if using) into a small saucepan.
Heat the mixture gently over medium-low heat, stirring occasionally, until it begins to steam and is fragrant — about 5 minutes. Avoid boiling to keep the milk creamy.
Remove from heat and strain the mixture through a fine mesh sieve into a bowl or measuring cup, pressing gently to extract all the flavorful liquids.
Stir in the molasses or brown sugar into the warm, spiced milk until fully dissolved and smooth.
Brew a shot of espresso or prepare ½ cup of strong coffee, then pour it into the warm spice mixture.
Whisk the mixture vigorously until well combined and slightly frothy.
Pour the steaming latte into a mug. Top with whipped cream or a sprinkle of cinnamon if desired for extra flair.
Enjoy immediately while warm, savoring the fragrant aroma and spicy-sweet flavor.