Heat 1 tablespoon butter and 1 tablespoon oil in a large saute pan over medium-low heat. Add onion, celery, parsley, capers, salt, and pepper; cook until tender, 8 to 10 minutes. Remove from heat; set aside; cool slightly.

In a large bowl, combine cooked salmon, mayonnaise, bread crumbs, mustard, dill, and eggs. Add sauteed vegetables, and stir well to combine.

With damp hands, form cakes using about 1/4 cup of salmon mixture. Heat remaining butter and oil in same saute pan. Cook cakes, in batches if necessary, until golden brown on both sides, about 3 minutes per side. Serve warm.