Gather all ingredients. Preheat oven to 400 degrees F (200 degrees C) with a rack positioned in the center.

Pierce potatoes all over with a fork and place on a large rimmed baking sheet lined with aluminum foil . Rub potatoes all over with olive and sprinkle evenly with 1 teaspoon of the salt and ¼ teaspoon of the pepper.

Bake in preheated oven until skin is crispy, and a fork can easily be inserted into centers of potatoes, about 1 hour. Let cooked potatoes sit at room temperature until cool enough to handle, about 10 minutes; reserve baking sheet with foil.

Cut cooled potatoes in half lengthwise and scoop flesh into a large bowl, leaving about ⅛-inch border around the edges; place potato skins, cut side up on reserved baking sheet; set aside.

Add heavy cream and butter to potatoes, mash until fully combined. Stir in chicken, carrots and peas, parsley, bouillon base, garlic, thyme, ¼ cup of the Cheddar cheese, remaining ¾ teaspoon salt, and ¼ teaspoon pepper until evenly combined.

Divide chicken mixture evenly between reserved potato skins (about ½ cup each) and sprinkle evenly with remaining ¾ cup cheese.

Bake at 400 degrees F (200 degrees C) until cheese is melted, about 10 minutes. Increase oven temperature to broil (do not remove baking from oven), and broil until cheese is browned, 3 to 5 minutes; garnish with additional parsley.