Cheesy potato patchwork pie

Name: Cheesy potato patchwork pie
Ingredients: 500g Maris Piper potatoes, unpeeled, cut into 1 cm thick slices; 1 tbsp neutral oil like rapeseed or sunflower; 1 tbsp butter, plus extra for the dish; 500g leeks, halved and sliced; 2 garlic cloves, finely sliced; 5 thyme sprigs; 2 bay leaves; 1 tbsp plain flour; ½ tsp ground mace, or a pinch of ground nutmeg; 1 tbsp Dijon mustard; 300ml milk; 50g parmesan or vegetarian alternative, grated; 100g extra mature cheddar, grated; steamed greens or watercress salad, to serve (optional); 250g plain flour, plus extra for dusting; 125g salted butter, cold and cut into cubes; 1 whole egg and 1 egg yolk (freeze the egg white for another recipe); 1 tbsp milk; 5 thyme sprigs, leaves picked