Prepare your cedar plank by soaking it in water for 30 minutes to 2 hours. Lay salmon on top of the cedar plank.
In a small bowl combine brown sugar, salt, pepper, and paprika. Rub the salmon with olive oil and then with the seasonings.
Set the grill to medium high heat and place the plank in indirect heat. Cover the grill and let the salmon cook for 15-20 minutes or until it reaches an internal temperature of 135 degrees. If you are cooking in direct heat, check the plank often and spritz with water if the plank catches fire. Remove the salmon from the grill.
To make the honey lime sauce: In a small saucepan add the butter over medium high heat. Let the butter melt until it starts to foam and turn slightly brown. Remove from the heat and whisk in lime juice and honey. Pour on top of salmon and serve.