Preheat your oven to 400°F (200°C).
In a large skillet, heat the olive oil over medium heat. Add the onions and cook until translucent.
Add the garlic and mushrooms, and sauté until the mushrooms are golden brown.
Stir in the carrots and peas, cook for a few more minutes.
Sprinkle the flour over the vegetables and mix well.
Gradually add the vegetable broth and almond milk, stirring continuously to form a smooth sauce.
Add the thyme, rosemary, salt, and pepper, then simmer until the sauce thickens slightly.
Transfer the vegetable mixture to a baking dish.
Cover the mixture with the puff pastry, trimming and crimping edges as necessary.
Bake in the preheated oven for 25-30 minutes or until the pastry is golden and flaky.
Let cool slightly before serving.