Place 1½ lb. skinless, boneless chicken breasts (about 4 medium) in a medium pot; pour in water to cover and season with kosher salt. Set over high heat and bring to a rolling boil. Remove from heat and let sit 15 minutes. Drain and transfer chicken to a cutting board; shred with 2 forks.

Meanwhile, whisk the garlic cloves, tahini, lemon juice, Dijon mustard, honey, salt, and ¼ cup water in a large bowl to combine and season generously with freshly ground pepper. Add shredded chicken, celery, red onion, jalapeño, parsley and dill, and dates and mix well. Season chicken salad with more salt and pepper if needed. Serve on butter lettuce leaves or toast.