Preheat the oven to 200°C/180°C fan/gas mark 6. Heat the oil in a large, non-stick frying pan over medium-low heat and cook the onion, celery and carrots for about 6 minutes until softened. Add the garlic and cook for a further minute. Increase the heat to medium-high, add the mushrooms and cook for a further 6 minutes.
Toast the nuts in the oven for 7 minutes. Set aside to cool. Then whizz in the food processor until coarsely ground.
Meanwhile, cook the red lentils according to the packet instructions. Drain well, then whizz in a food processor.
Combine the nuts, lentils and crumbled cooked chestnuts with the sautéed vegetables. Season to taste and leave to cool.
Once the mixture has cooled, roll out the puff pastry and leave on its paper. Form the mixture into a loaf that is about 3cm shorter than the width of the pastry. Lay the filling on the left-hand side, leaving a boarder of 1.5cm on the top and bottom, then fold the other half of the pastry over the filling and press down to encase it completely.
Brush the pastry with the almond milk, then place on a baking sheet and bake in the oven for 45-50 minutes, until the pastry is nice and golden.