Tomato, cream, heat, and just enough vodka to make the sauce tell the truth.
Vodka sauce has suffered under too many menus, and still it survives, because the idea is sound. Tomato wants richness. Cream wants acidity. Vodka slips between them and makes everyone behave.
This is not a pink sauce. It is a tomato sauce with a velvet coat and a little heat behind the eyes. Cook the paste until it darkens. Add the cream after the tomato has something to say.
Use ridged pasta. Smooth pasta lets sauce slide off like gossip off marble.
Start the aromatics. Cook onion in olive oil with salt until soft. Add garlic and chili for one minute.
Toast the paste. Add tomato paste and cook until brick red and darker at the edges. This is where the sauce earns itself.
Add vodka. Pour in vodka and stir until mostly evaporated. The pan should smell sharp, then suddenly round.
Cook pasta. Boil pasta until just shy of al dente. Save a mug of water.
Cream and toss. Stir cream into the sauce. Add pasta and splashes of water until glossy.
Finish. Add cheese off heat. Pepper hard. Serve immediately.
Tomato paste needs direct heat to caramelize its sugars and deepen its flavor.
Vodka helps dissolve flavor compounds in tomato that water and fat do not fully capture.
Pasta water and cheese bind the sauce so it clings instead of puddling.