Preheat oven to 350˚F.
Lightly grease a 2-quart baking dish with cooking spray and set aside.
Place quartered turnips in a large saucepan or stockpot; cover with water and add 1/2 teaspoon salt.
Set the stockpot over medium-high heat and bring to a boil; continue to cook at a steady boil for 10 minutes, or until very tender.
Drain the turnips; then, return them to the stockpot and set aside.
In the meantime cook the diced bacon in a skillet set over medium heat. Cook until crispy, about 5 to 6 minutes.
Using a slotted spoon, remove bacon from the skillet; do not discard the bacon grease. Set bacon aside.
Set the skillet back over medium-high heat and add 1/2 tablespoon butter to melt.
Add onions to the skillet and cook for 2 to 3 minutes, or until just starting to soften. Stir in garlic and cook for 20 seconds.
Add shredded brussel sprouts to the skillet and continue to cook for 4 minutes, or until tender. Remove from heat and set aside.
Place heavy cream, 2 tablespoons butter, salt, and pepper in a microwavable bowl or cup; microwave on HIGH for 1 to 1½ minutes, or until butter is melted and mixture is hot.
Mash the turnips with a potato masher.
Add the hot cream mixture to the turnips and continue to mash until combined and fluffy.
To the turnips add the Brussels sprouts mixture and half of the bacon; stir to combine.
Transfer turnip mixture to previously prepared baking dish.
Bake for 20 minutes, or until lightly browned and crispy on top.
Remove from oven; let stand 5 to 8 minutes.
Top with reserved bacon crumbles.