Season chicken with salt and pepper. Heat EVOO, a turn and a half of the pan, in a skillet with tight-fitting lid over medium-high heat. When oil is hot, add chicken in single layer and cook to light golden in color. Remove to a plate and reserve.
Add butter to skillet and melt. Add carrots, parsnips and shallots, and season with salt and pepper. Cover pan and soften vegetables, 2-3 minutes, stirring occasionally. Uncover pan and sprinkle in flour, stir 1 minute or so, then stir in stock, Worcestershire sauce, mustard and honey. Let thicken to coat spoon, add reserved chicken to heat through.
Serve with corn muffin alongside and garnish with parsley.