Preheat the oven to 325 F. On a large plate, stir together 1/4 cup flour, salt and pepper.
Turn the roast in the seasoned flour, shaking off any excess.
In a Dutch oven, heat 2 Tbsp butter and olive oil over medium-high heat.
Add the roast and cook, turning occasionally, until browned on all sides, about 8-10 minutes. Remove from the pan and set aside.
Add the pancetta to the pan and cook over medium-high heat until the fat is rendered and has become crisp. Use a slotted spoon to transfer to a paper towel and set aside.
Add onion, celery and carrots to the pan and sauté until soft, about 5 minutes.
Add garlic and stir until fragrant. Add mushrooms and cook, stirring occasionally, until most of the liquid has been released and evaporates.
Deglaze the pan by adding wine. Scrape up the brown bits stuck to the pan with a wooden spoon.
Stir in broth, tomato sauce or diced tomatoes, rosemary and basil, and bring to a simmer for a minute. Stir in the pancetta and season with a generous sprinkle of additional salt and pepper.
Place roast in the middle of prepared sauce and return to a light simmer. Cover with lid, place in the oven and cook util the roast is tender, about 4 hours (This can also be done in a slow cooker on low for 10 hours).
When done, transfer roast to a cutting board, cover with foil and allow to rest for 10 – 15 minutes.
While roast rests, mash remaining 2 Tbsp butter and 2 Tbsp of flour together in a bowl until forming thick paste. Stir mixture into dutch oven and cook over medium-high heat for 3 minutes or until the sauce thickens. Taste sauce and season with salt if necessary.
Cut roast into 1-inch thick slices, place into the sauce and serve over polenta or mashed potatoes.