Preheat the oven to 400 degrees. Scrub the potatoes and pierce the skins several times with a fork. Bake for 55 to 60 minutes, or until tender.
Allow the potatoes to cool slightly, then cut each in half lengthwise. Scoop out the pulp, leaving a 1/4-inch-thick potato skin; set aside the pulp in a medium bowl. Brush the potato skins with the oil, coating completely, and place on a large rimmed baking sheet.
Coarsely mash the potato in the bowl, add the chicken, broccoli soup, and 1 1/2 cups of the cheese blend;mix well and spoon equally into the potato shells. Sprinkle with the remaining 1/2 cup cheese.
Bake for 30 to 40 minutes, or until the edges are crispy and brown and the filling is heated through. Serve.