Preheat the oven to 200°C/180°C/gas mark 6. Cut the puff pastry into 4 equal rectangles then place on a flat baking sheet and score a border into each tart roughly 2mm deep. Bake for 6 minutes until just puffed up. Remove the layer of pastry in the middle that has puffed up, making sure you still have a layer of pastry on the base and the border is in place. Leave to cool.
Heat a large pan over a high heat and cook the bacon for 5 minutes until brown and crispy on both sides. Set aside on a plate lined with kitchen paper then lower the heat slightly and add the mushrooms and thyme. Cook for 5 minutes until golden brown, then set aside to cool.
To assemble the pies, lay 2 pieces of bacon across each one. Spread a quarter of the mushrooms on each, leaving a space in the middle. Place the mozzarella around the sides of each pie. Crack 1 egg into a small bowl and place in the middle of a pie, repeating with the remaining 3 eggs and pies. Brush the edge of the pies with the beaten egg and bake until the egg is just cooked still with a slight wobble and the cheese is melted. Serve with roasted cherry tomatoes.