Melt butter in a large frying pan over medium heat; stir in onion, celery, thyme, and bay leaf. Stir in the salt and pepper, and cook for about 1 minute, or until vegetables wilt slightly.
Stir in flour, then stir in milk and half and half. Bring mixture to a simmer and cook until it thickens, then add chopped turkey and nuts. Stir in brandy and cook for about 3 minutes longer, or until thoroughly heated. Remove and discard bay leaf, and season with salt and pepper.
Poach eggs in a pot of simmering, salted water in which a little vinegar has been added (vinegar makes the egg whites constrict quickly). Serve poached eggs over the hash, topped with shredded cheddar cheese.
Beverage pairing: Hanna Russian River Valley Chardonnay, California. With turkey and hash both being classic American foodstuffs, it’s wise to go with a classic American wine, like Chardonnay. But this one works beyond its tradition: It has the body to hold up against the cheese, eggs, and cream, as well as the acidity to balance them. Its clean citrus and tropical flavors will enhance the turkey, as well.
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