Heat the butter and oil in a medium pan over medium heat. Add onion and cook, stirring, until translucent, about 5 minutes. Add garlic and cook for 1 minute more.
Add rice, stir and cook for 3 minutes. Add the stock, salt and pepper, and bring to a boil.
Reduce heat to simmer, cover and cook for 10 minutes.
Season the salmon with salt, cumin and pepper. Add the salmon pieces in the partially cooked rice.
Cover and cook until the salmon is opaque throughout, about 10 minutes more or until the liquid is absorbed and the rice is tender but firm.
Add the heavy cream, cheese and fresh cilantro. Mix with a fork, cover and remove from heat. Let sit for 5 minutes and serve warm with lime wedges on the side.