Grease a 9x13-inch baking dish with coconut oil.

Toss the ground beef with 2 tbsp water, baking soda, 1 tsp sea salt, and 0.25 tsp pepper in a bowl until well combined; set aside for 20 minutes.

Meanwhile, place the turnips and 1 tbsp sea salt in a large saucepan; add water to cover.

Bring to a boil, then reduce to a simmer and cook until the turnips are tender, 8 to 10 minutes.

Drain the turnips and return to the saucepan over low heat, stirring constantly, to evaporate any remaining moisture, about 1 minute.

Remove from heat and mash the turnips smooth with a potato masher.

Stir in the olive oil.

Whisk the milk and egg yolk together in a bowl, then stir into the turnips.

Stir in the scallions; season with sea salt and pepper to taste.

Cover; set aside.

Heat the oil in a broiler-safe ten-inch skillet over medium heat until shimmering.

Add the onion and mushrooms and cook until the vegetables begin to soften, 4 to 6 minutes.

Stir in the tomato paste and garlic and cook until the bottom of the skillet is dark brown, about 2 minutes.

Stir in the Madeira, scraping up any browned bits, and cook until evaporated, about 1 minute.

Stir in the flour and cook for 1 minute.

Stir in the broth, Worcestershire Sauce, bay leaf, thyme, and carrots; bring to a boil, scraping up any browned bits.

Set aside once thickened.

Divide the beef into 2-inch pieces and place in a skillet over medium-high heat.

Cover and cook until the beef is cooked through, 10 to 12 minutes, stirring and breaking up meat chunks with two forks halfway through the cooking time.

Combine the arrowroot (or tapioca) and the remaining 2 tsp water in a bowl, then stir into the skillet.

Continue to simmer; stirring constantly, until the filling is slightly thickened, about 30 seconds.

Remove the thyme and bay leaf.

Season with pepper to taste.

Place the meat mixture in the prepared baking dish.

Spread the turnip mash evenly over the top of the beef mixture.

Adjust the oven rack to a position 6 inches from the broiler element and heat the broiler. Broil until the turnips are golden and the sauce is bubbling, 10 to 15 minutes. Allow to cool slightly; serve.

Don't Skip the Drying Step: The most common mistake with turnip mash is excess moisture, which leads to a soggy pie.

After boiling, be sure to return the turnips to the hot pan and stir constantly for that full minute. You want to see the steam disappearing to ensure a fluffy, potato-like texture.

The Baking Soda Secret: You might find the baking soda step unusual, but it’s a game-changer. This technique (often called "velveting") tenderizes lean ground beef, ensuring it stays juicy even after being sautéed and then broiled.

Don't rush the 20-minute resting period!

Watch the Broiler: Because this topping uses an egg yolk for color rather than the starch of traditional potatoes, it can brown very quickly.

Keep a close eye on the oven during the final 2-3 minutes to prevent the peaks of the mash from burning.

Thickening with Arrowroot: Unlike cornstarch or flour, arrowroot breaks down if it is cooked at high heat for too long. That is why we add the slurry at the very end of the meat cooking process. As soon as it thickens (which happens almost instantly), take it off the heat.

Make It Cheesy (Optional): If you aren't strictly Paleo and eat dairy, try mixing 0.5 cups of grated sharp cheddar or parmesan into the turnip mash before baking. It adds a delicious crust and boosts the fat content for Keto macros.

Turnip Bitterness: If you find turnips slightly too bitter, try swapping half the weight of the turnips with cauliflower florets. The cauliflower mellows the flavor while keeping the carb count low.