Place half the radish, turnips, parsnip pieces, and garlic in a gallon-size resealable plastic bag. Add soy sauce, sesame oil, olive oil, black pepper, salt, and red pepper flakes. Add remaining radish, turnips, parsnip, and garlic. Seal bag and mix to coat well. Let vegetables marinate on one side, about 10 minutes. Turn bag over and continue marinating, about 10 minutes more.
Pour marinated vegetables into a 1 1/2-inch deep baking pan; spread them into an even layer. Spread bacon and thyme evenly over the top.
Roast in the preheated oven until tender, about 55 minutes. Remove from oven, stir, and continue roasting until browned, about 15 minutes more.