Combine ½ cup flour, salt, pepper, and thyme in a resealable plastic bag. Add pork, toss to coat, then shake off excess. Brown half the meat in 1 tablespoons oil in a Dutch oven or large pot over medium-high heat, 7–9 minutes; transfer to a plate. Brown remaining pork in remaining oil and remove; reduce heat to medium.
Add onion, carrot, celery, garlic, and bay leaf to the pot; sweat for 5 minutes.
Deglaze pot with wine, simmer until nearly evaporated, then stir in broth and reserved pork. Bring stew to a boil, reduce heat to low, and simmer, covered, 30 minutes.
Stir in sweet potatoes, russets, turnips, and parsnips; cover and cook 30 minutes more.
Combine butter and 2 tablespoons flour and add to the stew; simmer 5 minutes to thicken. Remove bay leaf and season stew with salt and pepper.