Heat crab stock to boiling in a saucepan.
In another pot, heat olive oil and 2 Tbsp butter over medium heat. Add onion, garlic, and celery salt to taste, and cook for 15 minutes. Add rice and fry for a minute or two more.
Lower heat to medium low. Add the liquid from both cans of crabmeat and the dry vermouth, and cook, stirring constantly, until absorbed.
Add boiling crab stock one ladle at a time, stirring constantly and allowing each ladle to be absorbed before adding the next. This can easily take 45 minutes.
When the rice is fully cooked (but still with a soft bite) and the remaining 2 Tbsp of butter, the Parmesan, and the crab meat. Cover and remove from heat. Let sit, covered, 2 – 3 minutes.
Stir and serve sprinkled with smoked paprika.
