Adjust your oven racks to the lowest and middle positions and heat the oven to 450 degrees F. Heat a heavy-bottomed soup pot or Dutch oven over low heat.
Put the pork into a bowl and pour 2 T of oil over the meat. Season with salt and pepper and toss to coat well.
Increase the heat to med-high and wait until you see wisps of smoke starting to rise from the pot. Working in 2 batches, add pork and sear, turning only once, until 2 sides form a good brown crust - approx. 6-8 minutes per batch. Transfer the meat to a plate and set aside.
Add the onion to the pot, adding 1 T oil if the pan is dry, and cook while stirring, until softened - about 5 minutes. Add the garlic and thyme and cook until fragrant, approx. 1 minute. Whisk in the flour, then broth and wine. Return the pork to the pot. Using potholders, put a sheet of heavy-duty foil over the pot, pressing down on the foil so that it touches the stew. Seal foil around the edges. Put a lid on snugly andlet cook until you hear the liquid bubbling. Set pot on the middle rack of the oven and cook for 1 hour and 15 minutes. *45 minutes into the cooking, do the next step*
After 45 minutes, toss the sweet potatoes with the remaining 2 T of oil and a little salt and pepper into a 13 x 9 pan. Put that on the bottom rack and roast until the sweet potatoes and pork are tender, approximately 30 minutes longer. Remove the sweet potatoes and pork from the oven and stir the sweet potaotes into the stew , gently. Recover the pot with foil and lid and let the meat rest and sweet potatoes to marry with stew, about 15 minutes.Set stew over low heat, if necessary to reheat and then enjoy!