Thaw Bridgford dough in refrigerator overnight or quick thaw in the microwave as directed on package.
Preheat oven to 350 degrees Fahrenheit.
Remove papery peel from garlic and separate into individual cloves, chop two cloves and reserve. Cut just a little bit off the root end of all the other cloves. Place in an aluminum foil packet, drizzle with olive oil and sprinkle with sea salt. Place foil packet directly on the rack in the oven and bake until fragrant and roasted, 30-45 minutes. Remove roasted garlic and let cool.
Once roasted garlic is cool squeeze out of papery peels into a medium bowl with room temperature cream cheese, scallions, and reserved chopped garlic. Stir to combine.
Meanwhile, on a lightly floured surface roll defrosted dough to a 12” x 16” rectangle with the long side facing you. Use your hands to press into shape. Then dollop garlic cream cheese mixture onto dough and spread evenly, leaving a ¾” border along the top edge. Sprinkle roasted garlic cream cheese with chopped herbs and shredded cheese. Press filling slightly to adhere.
Carefully roll the dough into a tight cylinder starting with the long edge closest to you. Pinch the dough together to seal and carefully place it seal side down. Gently stretch and smooth the cylinder until it is even throughout before slicing with a sharp serrated knife into 12 even pieces.
Using a light hand arrange the rolls in a greased 13” x 9” baking pan. Top with a sprinkle of Parmesan cheese and red pepper flakes.
Let rise in a warm place until they have nearly doubled in size and are pressed against each other, 1 ½ to 2 hours.
Bake rolls in preheated oven until golden and puffed, 25 to 30 minutes. Brush with melted butter and sprinkle with sea salt. Let cool 10 minutes before serving.