Place the chopped celery in a large food processor and pulse about 5 times to break it down slightly.
Add the chopped cooked chicken to the food processor and pulse a few more times until the chicken is coarsely shredded into bite-sized pieces; avoid over-processing.
Push the chicken and celery to the bottom of the processor, then add the peeled hard-boiled eggs, sweet pickle relish, mayonnaise, and garlic powder.
Pulse the mixture in short bursts for about 10–15 seconds total, until evenly combined and the texture is lightly chopped but not mushy.
Taste and season with salt and pepper as needed.
Lightly butter and toast the bread if using, then assemble sandwiches with lettuce and a generous scoop of the chicken salad.
Cut sandwiches in half and serve immediately.
