Preheat oven to 375 degrees F. Wash and dry potatoes. Prick potatoes with fork. Place potatoes in oven for about 1 hour or until fork tender.
When cooked, halve the potatoes lengthwise. Carefully scoop out hot pulp, reserving 6 shells.
Mash potatoes with butter while still hot. Blend egg yolks and cream cheese or sour cream, mix with the scooped out potatoes, chives and salt. Mound mixture equally into each reserved shell.
Place back into the 375 degree F oven for about 10 minutes to heat through. Now evenly divide up the cooked broccoli flowerets onto the 6 stuffed potatoes and sprinkle a tablespoon of grated cheese on top of each broccoli topped stuffed potato. Place back into oven for about 5 minutes or until cheese is melted.