Heat a large Dutch oven or roasting pan over medium heat. Add the bacon and cook until the bacon is brown and the fat is rendered, 7 to 8 minutes. Remove the bacon with a slotted spoon and set aside to drain on a paper towel-lined plate. Set aside. Leave the pot on the heat.
Season the roast on all sides with the salt and pepper. Add the roast to the bacon fat remaining in the pan and sear on all sides until well browned, 8 to 10 minutes. Remove the roast from the pan and set aside. Add the onions to the pan and cook until wilted and fragrant, 2 1/2 to 3 minutes. Add the mushrooms and cook stirring occasionally until the mushrooms are soft and are beginning to color, about 4 minutes. Add the garlic, thyme, and bay leaf and cook, stirring, until fragrant, 45 seconds. Add the beer, beef stock, tomatoes and their juices, and the roast to the pan and bring to a simmer. Cover the pot tightly, place in the oven, and bake for 1 1/2 hours.
Carefully remove the roast from the oven and add the carrots, parsnips and turnips. Turn the meat, basting with the pan juices. Cover tightly and return to the oven. Bake until the meat shreds easily and the vegetables are tender, 1 1/2 to 2 hours, depending upon the size of the meat.
Remove and discard the bay leaf. Remove the roast from the pan and let sit on a cutting board until cool enough to handle. Using two forks or a knife and form, shred the meat.
Skim the fat from the pan juices and discard. Return the meat to the pan, add the parsley, and stir well.
To serve, spoon the polenta into wide entree bowls and spoon the pot roast, vegetables, and gravy on top.