Place chicken and pan drippings in a bowl. Without wiping pan, heat remaining 1 tablespoon oil over medium-high; add haricots verts, carrot, thyme, and garlic; cover, and cook, stirring occasionally, for 5 minutes or until tender. Add chicken and drippings back to pan; stir in peas. Sprinkle with remaining 2 tablespoons flour; stir to coat. Add chicken stock and bring to a boil; cook for 3 to 4 minutes or until thickened. Fold in parsley, pepper, and remaining 1 1/2 teaspoons salt. Whisk together egg and 1 teaspoon water in a small bowl.