Rinse lemon and orange and thinly slice them, discarding seeds; quarter the orange slices. Put fruit in a 4 to 5-quart saucepan.
Add honey, sugar, cloves & allspice to saucepan, stir frequently.
With a knife, cut the cinnamon sticks lengthwise into thinner strips. Add cinnamon sticks and 2 cups water to saucepan; bring to a boil over high heat, then reduce heat and simmer for 5 minutes.
Pour Prosecco into hot citrus base and heat until steaming, about 8 minutes. Keep warm over low heat. Ladle into heatproof cups or wine glasses and garnish with orange slices.