In saucepan, add water and bring to a boil. Peel turnips and cut into cubes. Place turnips in water and allow to cook until a fork is easily inserted.
While turnips are cooking, take skillet with lid and heat up butter and olive oil. Add in thinly sliced shallots and 2 cloves garlic, turning heat lower. Add half of the rosemary, and when fragrant, the sliced mushrooms.
Stir well until all mushrooms are covered, and allow to cook until slightly tender. Add balsamic vinegar and turn to low, covering with lid. Cook down until the vinegar is mostly reduced, giving a thicker paste and very saturated mushrooms.
Using either skillet or outdoor grill, cook steak to your liking. Remove from heat and allow to rest a few minutes.
While steak is resting, strain turnips, add remaining clove of garlic, tbsp of butter and heavy whipping cream (may need less if a thicker consistency is desired). Mash well until potato texture. Salt and pepper to taste.
Plate steak with a helping of smashed turnips. Heap a portion of the mushrooms over each steak and garnish with remaining rosemary. Enjoy!