Make the vanilla-cinnamon syrup: In a small saucepan, combine water, sugar, and cinnamon stick. Bring to a simmer over medium heat, stirring until sugar dissolves completely, about 2 minutes. Remove from heat, stir in vanilla extract, and let steep for 10 minutes. Remove cinnamon stick and let syrup cool.
Brew 2 shots of espresso using your espresso machine, moka pot, or strong coffee maker. Pour the hot espresso into your favorite mug.
Add 2 tablespoons of the vanilla-cinnamon syrup and 1/4 teaspoon ground cinnamon to the espresso. Whisk vigorously for 10 seconds until the cinnamon is fully incorporated and no longer floating.
Heat the milk in a small saucepan over medium heat or in the microwave until steaming hot but not boiling, about 150-160°F if you're using a thermometer.
Froth the hot milk using a handheld frother, French press (pump the plunger up and down 10 times), or by shaking vigorously in a sealed jar for 30 seconds until you see foam forming on top.
Pour the frothed milk over the espresso mixture, holding back the foam with a spoon. Then spoon the foam on top to create that signature latte look.
Dust the top with a pinch of ground cinnamon for garnish. Serve immediately while hot and enjoy your café-quality latte at home.