Melt 4 tbsp butter in a pot over medium heat.
Add onions, thyme, bay leaves, 1½ tsp salt, and pepper.
Cook, stirring often, for 35–45 minutes until deeply caramelized.
Stir in the remaining 2 tbsp butter, carrots, celery, and garlic. Cook for 5 minutes.
Season chicken with remaining salt. If using thick breasts, butterfly them.
Add wine and sherry to deglaze the pot. Cook for 2–3 minutes.
Sprinkle in flour and stir constantly for 1 minute.
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