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.