Remove the beef from the pan, then cook the onion until soft before adding the grated carrot and garlic, sautéing until everything becomes tender and fragrant.

Return the beef to the pan and stir in the flour, cooking briefly before adding the tomato paste, thyme, Worcestershire sauce, and red wine, letting it cook down to remove the alcohol flavor.

Add the peas and beef stock, season with salt and pepper, and bring the mixture to a boil before reducing the heat and simmering until thick and rich.

While the filling cooks, boil peeled and chopped potatoes in water until soft, then drain thoroughly and return them to the pot.

Add dairy-free butter, salt, and pepper, then gradually mix in the dairy-free milk while mashing until smooth and creamy.

Transfer the beef filling into a casserole dish and spread it evenly, then layer the mashed potatoes on top and smooth them out completely.

Use a fork to score the top of the potatoes, then bake until golden brown and bubbling around the edges.

Allow the pie to rest briefly before serving so it holds its shape when sliced.