1. In a food processor, pulse 1 bun until fine crumbs form (you should have about 1/4 cup). Transfer breadcrumbs to a large bowl and add salmon, celery, shallot, and mayonnaise. Season with salt and pepper; mix well to combine. Form into a 3/4-inch-thick patty, transfer to a plate, and refrigerate 10 minutes.

2. In a medium nonstick skillet, heat oil over medium. Add patty and cook, flipping once, until browned and heated through, about 8 minutes.

3. Meanwhile, split and toast remaining bun. Serve burger on bun with mayonnaise and spinach.