Season and cook the chicken. Pat chicken pieces dry with paper towels and season generously with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken in a single layer (work in batches if needed) and cook for 3-4 minutes until golden brown but not fully cooked through. Remove to a plate.
Sauté the mushrooms and onions. In the same skillet, add remaining tablespoon of oil and butter. Once butter melts, add onions and cook for 2-3 minutes until softened. Add mushrooms and cook for 5-6 minutes until they release their moisture and begin to brown. Season with a pinch of salt to help draw out moisture.
Add aromatics and create a roux. Add garlic to the skillet and cook for 30 seconds until fragrant. Sprinkle flour over the mixture and stir constantly for 1 minute to coat the vegetables and cook off the raw flour taste.
Build the sauce base. Slowly pour in chicken broth while stirring continuously to prevent lumps. Add Dijon mustard, paprika, and thyme. Bring to a simmer and cook for 2-3 minutes until slightly thickened.
Return chicken to finish cooking. Add the chicken back to the skillet along with any accumulated juices. Simmer for 3-4 minutes until chicken is fully cooked through (internal temperature of 165°F).
Incorporate the sour cream carefully. Reduce heat to low. Take a spoonful of the hot sauce and stir it into the sour cream to temper it. Then gradually add the tempered sour cream to the skillet, stirring constantly. Heat just until warmed through – do not boil after adding sour cream or it may curdle.
Taste and adjust seasoning. Add salt and pepper as needed. If the sauce is too thick, add a splash more broth; if too thin, simmer for another minute.
Serve immediately over cooked egg noodles. Garnish with fresh parsley.