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Heat the olive oil in a large, heavy-based pan on medium-high heat.
Add the onions, garlic, carrots and celery. Cook for 4-5 minutes, stirring regularly until softened.
Add the beef mince and cook, stirring, breaking it up as you go, until it begins to brown, for a further 4-5 minutes.
Stir through the tomato paste followed by the plain flour.
Once the flour is incorporated, add the beef stock, Worcestershire sauce, thyme and potatoes to the pan. Bring to a simmer and then reduce the heat to low. Season with salt and pepper (the amount you use will depend on how salty your stock is; I use at least 1 teaspoon of salt and ¼ teaspoon of pepper).
Cook, covered for 30-35 minutes or until the potatoes are tender. Stir occasionally and add ½ cup of water halfway through if the sauce is beginning to stick to the base of the pan (see note 1 for tips).
Turn the heat off and stir through the frozen peas (they will heat through in the oven).
Allow the mixture to cool slightly.
Preheat the oven to 200°C/400°F (180°C fan-forced).
Spoon the cooled mixture into an oven-safe 1.5L (roughly 1.5 qt) baking dish.
Layer the pie with the thawed puff pastry rectangles so that they slightly overlap each other.
Brush with the egg, sprinkle with sesame seeds and bake for 30-35 minutes or until crisp and golden.
Allow to stand for 10 minutes before serving.