Peel turnips, making sure to remove the tough top bits; place in a saucepan.
Cover with water and bring to a boil.
Cover with pan lid, lower heat and simmer for about an hour until tender.
Drain then cut into chunks small enough to fit in your food processor.
Place chunked veggies, butter, and sour cream in a food processor and puree.
Add beaten eggs and cheese and whir some more until ingredients are well-mixed (it won't take long).
Pour into casserole dish and bake for about 20 minutes at 350°F until it's a little brown on top and edges (or you can nuke it for about 7-10 minutes).
You might want to experiment the first couple of times you make it to see how brown you like the top.
You can sprinkle a little more cheese on the top before baking, if you like.
(You can also cube the turnips ahead of time then simmer and it doesn't take so long to cook, but some turnips are so hard to cut when raw that I've given up on that technique and just boil them whole.) Optional: add a garlic clove to the cooking veggies and puree along with everything else; adds.
25 carbs to each serving.
Other options: 1/4 tsp dill, crumbled bacon, etc.
Fluffier than other mashed-potato substitutes, because of the egg baked inches.
The carb count on these might be a bit off, but they wouldn't be much more.