Preheat the oven to 200ºC/400ºF/gas 6. Line a large baking tray with greaseproof paper.
Peel and finely chop the onion, then trim and finely chop the celery. Heat 1 tablespoon of olive oil in a large frying pan over a medium-high heat, then add the chopped veg. Cook for 10 to 15 minutes, or until golden. Meanwhile, finely chop the mushrooms.
Peel and crush in the garlic, then add the chopped mushrooms. Cook for a further 5 minutes, or until the mushrooms start to soften. Add the mustard and wine, season with salt and pepper, then reduce the heat to low. Cook for 5 to 10 minutes, or until all the liquid has boiled and bubbled away. Set aside to cool.
Add the cooled mushroom mixture and breadcrumbs to a large bowl. Pick, finely chop and add the parsley leaves, then pick in the thyme leaves. Stir well to combine, then season to taste.
Cut the sheets of puff pastry in half lengthways so you have four equal-sized pieces. Spoon a quarter of the mushroom mixture along the middle of one length of pastry, moulding it into a long sausage shape with the back of a spoon.
Brush the almond milk along the pastry edges, then carefully fold one of the long sides of the pastry up over the filling. Press the edges to seal, then crimp with a fork. Repeat with the remaining ingredients until you have four long rolls, then cut each length into four pieces.