Heat the vegetable oil in a large pot over medium heat. Add the pork cubes and cook until browned on all sides, about 5 to 7 minutes.
Add the sliced onions to the pot and cook for 3 minutes until they start to soften.
Stir in the turnip cubes and cook for another 3 minutes, stirring occasionally.
Add the chopped apples, chicken broth, dried thyme, salt, and black pepper. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 45 minutes until the pork is tender and the turnips are soft.
Remove the lid and simmer uncovered for 10 more minutes to thicken the broth slightly. Stir once or twice during this time.