Bring a large pot of salted water to a boil. Cook the rigatoni according to package directions.
In the meantime, brown the chorizo in a large frying pan over medium heat, breaking it up with a spatula as it cooks. This should take about 7 to 10 minutes.
Lower the heat to medium-low. Add butter and heavy cream to the pan and stir to combine, until the butter has melted and the mixture is lightly steaming.Next, add the shredded cheese in batches, stirring constantly to melt.
Once all the cheese has been incorporated, season the sauce with salt and lime juice.Drain the pasta and add the noodles to the sauce. Stir to combine, then serve hot.
Notes
Chorizo: We recommend using a high quality brand of Mexican chorizo, like Cacique Pork Chorizo, for the best flavor. Make sure to buy ground chorizo, not links.Soyrizo alternative: We love making this pasta with soyrizo (soy chorizo) for a lighter - and also vegetarian - version. If you use soyrizo, make sure to cook according to the package instructions as it typically doesn't need to cook as long as chorizo.Cheese:Always buy blocks of cheese and shred it yourself for the best texture. We love our box grater (linked above in the Equipment section) and use it all the time!Making the sauce: Building the sauce around the chorizo is absolutely crucial to developing the flavor of this dish! If there's too much grease in the pan after browning the chorizo, carefully drain some out first.Serving suggestions: This pasta is pretty heavy, so it can definitely stand alone. But you can also serve it with a side salad or fresh bread and dipping oils if you'd like.Storing and reheating: Store leftover chorizo pasta in an airtight container in the fridge for up to 4 days. Reheat single servings in the microwave for about 2 minutes, stirring halfway through.