Line a large platter or baking sheet with parchment paper.
Heat the olive oil in a medium skillet over medium heat.
When the oil begins to shimmer, add the sausage in small pieces and cook, breaking up the meat with a spoon as it cooks, until lightly browned, about 3 minutes.
Add the onion and cook until softened and translucent, about 10 minutes.
Add the chicken livers and stir, breaking them up with a wooden spoon, until cooked, about 5 minutes.
Add the rice and stir to coat. Continue stirring until the rice is lightly toasted and becomes translucent, about 2 minutes, then add the wine.
Stir until the alcohol aroma dissipates, about 1 minute, then add 1 cup of the broth.
Cook, stirring continuously to prevent the rice from sticking to the pan, until the broth has been absorbed, about 3 minutes.
Add the tomato sauce and cook, stirring continuously, until it has been absorbed, 5 minutes more.
Add another 1/2 cup broth, stirring continuously, until it has been absorbed, 8 to 10 minutes. If, once the rice has absorbed the broth, more liquid is needed, add the remaining 1/2 cup broth. The rice is done when it is al dente.
Remove the pan from the heat and stir in the basil (if using), Pecorino Romano, and butter. Season to taste. Spread the rice over the prepared baking sheet and refrigerate until cool, about 1 hour.