Preheat the oven to 200°C (fan) / 400°F / Gas Mark 6. Bring a saucepan of water to the boil.
Cut the baby potatoes into pieces. Remove the ends of the Tenderstem and separate the florets from the stems, (set aside the florets for now). Cut the stems into pieces 3-4cm long. Boil the potatoes and Tenderstem stems for 3-4 minutes.
Meanwhile, trim the ends of the asparagus and cut the stalks into pieces. Split the Tenderstem florets into bite-sized pieces. Add these to the saucepan along with the frozen peas, and cook for a further 2-3 minutes - they don't need to be fully cooked through as they will continue cooking inside the pie. Drain and set aside.
Melt the vegan butter in a frying pan. Trim and slice the leek. Add to the pan, and cook gently for 3-4 minutes until soft.
Add the flour to the leek, and stir until no lumps remain. Add the vegetable stock and simmer gently until thickened.
Meanwhile, remove any woody stems from the kale and chop roughly, finely chop the parsley, and slice the spring onions.
Add the vegan cream to the pan.
Stir in the kale, parsley, spring onions, mustard and the juice of the lemon. Remove from the heat. Add salt and black pepper, taste and adjust seasoning as required.
Unroll the puff pastry, then using your pie dish as a template, cut it just a little larger than required. Tip the pie filling into the pie dish.
Brush the underside of the pastry with water around the edges, then place it over the pie filling, pushing down the edges or crimping with a fork to seal. Use a knife to trim any excess pastry from the edges.
Make the pastry glaze by mixing the dairy-free milk and soy sauce, then brush all over the pastry. If you like, you can use a sharp knife to make a pattern on the top of the pie at this point.
Bake the pie for 25-30 minutes until the pastry is golden and crisp throughout - you can lift up a corner of the pastry to check if necessary. If the pastry is turning too brown too quickly, just cover the top with foil.