Place red potatoes and sweet potatoes in a 7-qt. slow cooker. Add roast, broth, pearl onions, garlic; season with salt and pepper. Place corn around roast and add water. Cover and cook on high heat 6 to 7 hours.
Transfer roast to a shallow bowl, leaving slow cooker on, but now turned to low. When roast is cool enough to handle, cut into cubes.
Skim fat from cooking liquid. Smash some of the potatoes in slow cooker. Add cubbed roast. Dish up using bowls and top pot roast with a dollop of sour cream and a handful of grated carrots.