Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
Arrange one sheet of puff pastry on a work surface with the long side facing you.
Spoon half of the vegetable mixture lengthwise across the lower-half of the pastry, leaving a 2- to 3-inch (5 to 8 cm) border, pressing the mixture together with your hands to form a roll.
Fold the sides of the pastry over the filling, then roll it up, starting at the end closest to you. Repeat with the second Wellington.
Place the Wellingtons on the prepared baking sheet, leaving space between them.
Lightly brush the Wellingtons with the melted vegan butter.
Bake until golden brown, 25 to 30 minutes.
Transfer the Wellingtons to a long plate or a platter and garnish with the fresh thyme sprigs. To serve, cut into thick slices using a large, sharp knife.