Melt butter in a large skillet over medium-high heat. Add mushrooms and salt. Saute until mushrooms release their moisture. Continue cooking until moisture evaporates and mushrooms begin to brown, 8 to 10 minutes. Add shallots; cook and stir just until shallots soften, 3 or 4 minutes.
Reduce heat to medium. Stir in flour to coat the mushrooms; cook until flour begins to turn golden, about 5 minutes, to form roux. Add peppers; cook and stir about 1 minute. Pour in sherry wine; allow to sizzle about 30 seconds. Stir in stock. Raise heat to medium-high and bring to a simmer. When it starts to bubble, reduce heat to medium-low and cook until slightly thickened, 10 to 15 minutes stirring occasionally. Add nutmeg and cayenne pepper.
Stir in thyme, parsley, cream, and chicken. Reduce heat to low and cook until chicken is heated through, about 5 minutes. Check seasonings and adjust as needed. Top each serving with some chopped fresh chives.