Bring a six-quart pot to broil. Add the turnips, potato, and sugar. Boil for about 30 minutes or until turnips and potato are tender.
Meanwhile, dredge bangers in flour and over medium heat, sauté the onions and bangers in a large skillet together with a little olive oil together until the bangers are brown and crispy.
Pour over the wine and broth and scrape the bottom of the skillet to deglaze.
Add lingonberry jam, and thyme. Salt and pepper to taste, and turn heat to low.
When turnips are done, drain the water and mash up with a potato masher. Add butter and broth and mash until you get the consistency you like.
Plate the bangers over the mash and top off with sauce.