In a pan over medium heat, add 3 tbsp of the butter and let melt.
Add the grated ginger and cook, stirring, for 1 minute, until foamy and just lightly golden.
Pour in the tomato passata and add a pinch of salt, then bring to a gentle bubble. Reduce the heat all the way to low and let simmer for 15 minutes, stirring occasionally.
Meanwhile, bring a pot of heavily salted water to a boil. Add the rigatoni and cook according to package instructions, until al dente.
Transfer the rigatoni directly into the sauce along with ½ cup of starchy pasta water, then stir to coat. Add a little bit more pasta water as needed if you’d like to loosen the sauce. Finish by melting the remaining tablespoon of butter into the sauce.
Serve with lots of finely grated pecorino on top!