Add the rice and water to a pot, and over medium heat, let them come to a boil.
Once rice and water have started to boil, cook for 8 minutes, stirring often.
At this point, add the milk, sugar, orange peel and cinnamon sticks.
Still on medium heat, cook the rice mixture for 30 minutes, stirring often so that the rice doesn't stick to the pot, until the rice is cooked and most of the liquid has absorbed. If rice is cooking too quickly, turn the heat down slightly.
At this point, remove the orange peel and cinnamon sticks.
Turn heat down to low, add butter to the rice, and cook for 7-10 minutes until all the liquid has absorbed and the mixture is dense in consistency.
Add the rice to a shallow square dish, level it out, and cover with saran wrap. Let it cool.
If your ricotta is very moist and has a lot of liquid in it, drain it with a colander.
In a big bowl, add ricotta, beaten eggs, fior d'arancio, and cinnamon. Mix with a wooden spoon or whisk until all ingredients are combined.
Once the rice mixture has cooled completely, add it to the ricotta mixture, slowly, a few spoons at a time. Mix with a wooden spoon until the rice is fully incorporated into the mixture. Set the filling aside.