Preheat oven to 350 degrees F (175 degrees C).

Pour the milk into a saucepan along with the lemon zest and cinnamon sticks. Bring to a simmer over medium-high heat, then reduce heat to low, and cook for 5 minutes. Turn heat off, and allow to steep for 15 minutes.

Gently beat the eggs and sugar together until the sugar has dissolved. Slowly beat in 1 cup of the hot milk, a little at a time, until it has been incorporated. Stir the egg mixture back into the hot milk, pour in the pisco, and mix until well combined.

Pour the custard through a fine mesh sieve into a 2-quart ceramic casserole dish to remove the lemon zest and cinnamon. Bake in preheated oven until set, and browned on top, about 30 minutes. Chill before serving.