Heat a small skillet over medium heat with a drizzle of oil. Add carrots and celery, and sauté 8-10 minutes. Raise the heat a bit, add vinegar, celery salt and sugar, and swirl to evaporate the vinegar. Add the dill and remove from heat.
Cut iceberg into wedges and remove the core. (Reserve remainder for a chopped salad on another night.) Trim iceberg slabs or wedges to sit flat on plates or a platter.
Season chicken with salt and pepper on both sides.
Heat a cast-iron griddle or large skillet over medium-high heat with olive oil, 1 turn of the pan. Working 2 pieces at a time, cook chicken until brown then remove to plate. Add remaining tablespoon of oil to the pan and repeat with remaining chicken. Cover the chicken with foil to keep warm.
Add butter to skillet. When it foams, add garlic, swirl 1 minute then add Worcestershire and hot sauce. Add chicken in Buffalo sauce, turning to coat, and let heat through, 1 minute more.
Top the lettuce with chicken, carrots and celery, some blue cheese and scallions, and serve.
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