Heat a large sauté pan over medium heat, add the olive oil and heat through. Add the butter and allow to melt then add the onion, celery and bell pepper and sauté until the vegetables are tender, about 6 minutes. Remove from heat and cool.
In a large bowl combine the sautéed vegetables, mayonnaise, breadcrumbs, lemon juice, and Worcestershire. Gently fold in the crabmeat, so it is combined but stays in some larger pieces.
If one side of the salmon is higher than the other, trim some of the top so that it’s fairly even and reserve for another use. Cut the salmon in half lengthwise and season with salt and pepper.
Divide up the crab filling and place on top of each piece of salmon, then evenly spread it over the salmon.
If one side is wider, start there then roll the salmon up into a pinwheel shape. If needed you can use toothpicks to secure the pinwheels. Cut each roll in half so you have 4 thinner pinwheels.
Arrange the salmon pinwheels on a baking sheet. Bake until the fish is just cooked through and flakey, about 15 to 18 minutes. Serve hot garnished with the remaining parsley and chives.