Chicken pie with carrot and peas

Name: Chicken pie with carrot and peas
Cuisine: European, British
Ingredients: 4 x 180g skinless chicken breasts; a knob of butter; C bunch of spring onions; 150g button mushrooms; 1 heaped tablespoon plain flour, plus extra for dusting; 2 teaspoons English mustard; 1 heaped tablespoon crème fraiche; 300ml organic chicken stock; a few sprigs of fresh thyme; % of a nutmeg, for grating; 1 sheet of pre-rolled puff pastry; 1 egg; 600g carrots; few sprigs of fresh thyme; 2 little gem lettuces; A knob of butter; 1 tablespoon flour; 300ml chicken stock; 2 sprigs of fresh mint; 480g frozen peas; 1/2 a lemon