Melt the butter in a large pan over moderate heat. Add shallots and garlic and cook gently until softened but not browned, approx. 5-7 minutes. Add the Portobello mushrooms and cook until there is little moisture remaining in the pan, about 10 minutes.
Add the plant-based meat and the cream and bring the mixture to a simmer. Stir in the mustard and lemon juice and cook until the mixture has thickened and reduced. Make sure all the liquid has evaporated; you want this filling fairly dry. Finely chop the tarragon leaves and stir into the mixture before seasoning with salt and freshly ground black pepper. Transfer the mixture into a bowl and leave in the refrigerator, covered, to cool completely, at least 1 hour.
Lay out a double layer of plastic wrap on a clean work surface. Tip the chilled mushroom mixture onto the bottom half of the cling wrap and shape it into a log shape. Working from the bottom, use the plastic wrap to gently roll the mixture up to form a tight and compact roll. Twist the ends of the plastic wrap to secure. Return to the refrigerator to chill and firm up. You can prepare this the day before and leave it in the refrigerator overnight.
When ready to cook, make the spinach pancakes. Cook the spinach in a large pan with a small amount of water over moderate heat until wilted. Transfer the cooked spinach onto a clean tea towel and ring out any excess moisture before finely chopping. Set aside.
For the pancake batter, mix flour, baking powder, and salt in a medium bowl. Add the oil and soy milk and mix into a slightly lumpy batter. Add the cooked spinach and season with salt. Adding small amounts of butter to a clean, non-stick pan, cook thin pancakes. You should be able to get about 8 3" pancakes. Set aside to cool.
To build the Wellington, open the sheet of puff pastry onto plastic wrap. Lay the cooled pancakes on top of the pastry, slightly overlapping, in a rectangle of 2x4 pancakes. Remove the cling wrap from the chilled mushroom log and place on one end of the pancakes. Working from the bottom up, roll the pastry around the spinach pancakes and mushroom log until the pastry meets on the other side. Pinch the Wellington closed to seal completely and trim off any excess pastry. Twist the ends of the plastic wrap to make a tight log. Spend a little time shaping your log so it is even and looks nice. Place in the refrigerator for 5 minutes to chill.
Preheat the oven to 375°F. Unwrap the Wellington and place on a baking sheet lined with parchment paper. Brush all over with a bit of soy or oat milk and make some decorative cuts in the top to allow the steam to escape. Bake for 35 minutes then raise the temperature to 400℉ and bake for another 10 minutes or until it is browned all over. Remove and leaving to rest for 10 minutes before slicing and enjoying. Serve with mushroom gravy.