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Step 1
Heat olive oil in a large saucepan over high heat, add chicken and brown all over (4-5 minutes). Add thyme, bay leaves and 2 litres cold water, bring to the boil. Reduce heat to medium and simmer until chicken is tender (40-45 minutes). Drain liquid into a bowl and reserve 500ml (freeze remainder for another use.). Cool chicken, then coarsely shred flesh (discard skin, bones and sinew) and refrigerate until required.
Step 2
Melt butter in a saucepan over medium-high heat, add onion and carrot, sauté until tender (8-10 minutes), then add flour and cook, stirring, for 3 minutes. Add reserved cooking liquid a little ata time, whisking to combine, then stir continuously until mixture boils and thickens (3-4 minutes). Add shredded chicken, stir to combine, then add herbs, stir and season to taste. Cool to room temperature, then refrigerate until required.
Step 3
For cornmeal pastry, combine flour and polenta in a bowl, and rub in butter until just combined with streaks of butter still visible. Make a well in the centre, add 350ml cold water and mix to incorporate, then knead until smooth. Wrap in plastic wrap and refrigerate to rest (at least 1 hour).
Step 4
Preheat oven to 180C. Roll out two-thirds of pastry on a lightly floured work surface to a 5mm-thick round and line a 20cm-diameter cake tin, allowing edges to overhang a little. Roll out remaining dough to a 5mm-thick round large enough to fit on top of cake tin and set aside.
Step 5
Spoon filling into lined cake tin, then fold edges inward and place pastry lid on top, pressing to seal. Cut a small cross in the middle of the pie, brush top with eggwash and bake until golden brown (1 hour to 1 hour 10 minutes). Cool slightly before turning out onto a serving plate and serve warm or at room temperature with Dijon mustard on the side.