Make the mashed potatoes: Bring 4 cups (960 ml) of water and 1 teaspoon of salt to a boil in a large saucepan and add the potatoes. Lower to a simmer and cook until the potatoes are fork-tender, 20 to 25 minutes. Drain the potatoes, reserving about ¼ cup (60 ml) of the boiling water.
Using a potato ricer or food mill, rice the potatoes into the pot with the remaining cooking water. Add the butter and mix well, until melted. Add the milk and salt and pepper to taste and place over low heat. Mix vigorously with a wooden spoon until the potatoes are smooth and creamy. Set aside.
Make the filling: Heat the olive oil in a large, deep frying pan or Dutch oven and add the carrot. Cook for 6 to 7 minutes, or until the carrot begins to brown, then add the onion. Cook for 5 to 6 minutes, or until the onion begins to soften and become translucent, then add the mushrooms and fry until lightly brown, 4 to 5 minutes. Add the garlic and fry 1 minute more.
Add the alternative meat and break it up using a wooden spoon. Brown the crumbles, mixing well with the other ingredients. Stir in the tomato paste, pimenton, cumin and allspice and cook for 1 to 2 minutes, stirring. Add the Worcestershire sauce, vegetable stock and stout and mix well. Simmer until the mixture is reduced by one-third, about 5 minutes, and then stir in the peas. Season with salt and pepper to taste and mix well.
Preheat the oven to 350°F (177°C). Pour the meat mixture into an 8 x 8–inch (20 x 20–cm) casserole or Pyrex® dish. Scrape the mashed potato topping over it, smoothing over the entire surface of the filling mixture with the back of the spoon or with a tiny offset spatula. Sprinkle the top with paprika.
Bake the shepherd’s pie for 15 minutes, or until the edges of the potatoes begin to lightly brown. Alternatively, you may cover the casserole with tinfoil and refrigerate overnight before baking and serving. Serve hot.