Set up your oven’s temperature to 400 degrees Fahrenheit and let it preheat. With 2 tablespoons of olive oil, brush the bottom and sides of a 1.5-quart baking sheet.
Cut each salmon filet lengthwise, leaving ½ an inch of uncut space on each side and bottom; make a pocket by carefully putting the point of a sharp knife under each flap, leaving ½ inch space on each side.
Mix the crab meat, butter, rice, cream cheese, garlic, and herbs (excluding salt and dill) in a medium mixing bowl. Fill each filet pocket with this filling mixture, leaving a little mound at the top. Brush the salmon with the remaining olive oil, season with salt and dill, and arrange in a baking dish.
Bake the stuffed salmon for 20 minutes, checking for doneness about 2 minutes before the end of the cooking time (by this time, the thickest section of the filet will flake).