Chicken, mushroom and wild garlic pie - Gluten-Free Heaven

Ingredients

• 560 6 gluten-free plain/all-purpose flour
• 2 tsp xanthan gum
• 1 tsp salt
• 280 g unsalted butter (chilled)
• 2 large free-range eggs (beaten)
• 1 brown onion (peeled, finely diced)
• 1 small carrot (peeled, finely diced)
• 70 g young wild garlic leaves (if out of season, replace with spinach plus 1 large garlic clove, minced)
• 250 g chestnut mushrooms (chopped into small pieces)
• 350 g cooked chicken (I use leftover roast chicken, but pan-fried chicken breast/ thighs also work well), cut into bite-size pieces)
• 60 g unsalted butter (plus extra for greasing)
• 60 g cornflour/cornstarch
• 1 tbsp wholegrain mustard
• 360 ml gluten-free chicken stock/bouillon
• 60 ml white wine
• 120 ml single/light cream
• 60 ml whole milk
• 1 free-range egg
• 1 tsp milk