Preheat oven to 400°F (200°C) and line baking sheet with parchment.
Heat olive oil in skillet; sauté onion and garlic for 3 minutes.
Add mushrooms; cook until liquid evaporates, about 7 minutes.
Stir in soy sauce, thyme, parsley, salt, and pepper. Remove from heat.
Roll puff pastry on lightly floured surface; cut into 12 squares.
Place spoonful of filling in each square.
Fold corners over filling, sealing edges gently.
Brush tops with plant-based milk.
Arrange bites on baking sheet.
Bake 18–20 minutes, until golden and puffed.