Place cubed sweet potatoes in large pan with just enough water to cover. Bring to a boil over medium-high heat, then reduce heat to medium-low. Cover and cook about 15 minutes, until they are just tender.
While potatoes are cooking, poach the chicken: Cut breasts in half vertically, place them in a large skillet and add just enough water (or low-sodium chicken broth) to cover. Bring to a boil over medium high heat, then reduce heat to low and cook for about 10 minutes, until chicken is just cooked through and tender. Drain, transfer to work surface and cut into 1/2 cubes. Set aside.
Drain potatoes and set aside.
Clean out skillet and melt butter over medium heat. Add the onion, bell pepper and garlic, and cook for 3 minutes, stirring constantly, until vegetables have softened. Add paprika and dried thyme, crumbling it between your fingers, then the salt and pepper to taste. Stir to combine for 1 minute. Add chicken, sweet potatoes, scallions, parsley and half-and-half. Cook for 6 to 8 minutes, until liquid has reduced and hash is thickened and "tight.".