Melt 2 tablespoons of the butter in a large frying pan over medium heat. Add 1 pound cubed chicken breast and 1 1/2 cups trimmed and peeled pearl onions. Season with 1 teaspoon of the kosher salt. Cook until lightly browned, stirring occasionally, about 5 minutes. Transfer to crock pot.
Return pan to medium heat and melt remaining 2 tablespoons of butter. Add the 8 ounces quartered mushrooms and cook until lightly browned. During the last minute or so of cooking, sprinkle mushrooms with the 2 tablespoons flour. Stir to coat mushrooms in the flour and toast, cooking about a minute or two longer to get rid of the raw flour taste. Transfer to the slow cooker with the chicken.
Deglaze the skillet with the 1 cup white wine, scraping up any browned bits. Add that to crock pot. Finally add to the crock pot, 1 cup cream, 3 sprigs fresh thyme, last 1 teaspoon salt, 1 bay leaf, 1/2 teaspoon white pepper, and 1/4 teaspoon nutmeg. Cook on high, 4 hours or low 6 hours.
Remove thyme sprigs and bay leaf. Taste and season with more salt if needed. Serve with steamed green beans and buttered egg noodles and sprinkle with chopped parsley.