Add cream cheese, cooked broccoli, shredded cheddar and half of the garlic salt to a bowl and mix until combined.
Unroll crescent rolls, cut and divide into 4 pieces. (If you’re using crescent roll dough and not a sheet, use your fingers to smooth out any holes so that each one is smooth and doesn’t have any perforations on it.)
Add ¼ of the cream cheese to the long side (kind of like a hot dog shape) of each one of the crescent dough rectangles and roll them like cigars - pinching the ends shut.
Wrap them into bagel-like circles and place on a lined or sprayed baking sheet.
Brush the top of each one with a little bit of beaten egg and then sprinkle evenly with the remaining cheese and the remaining garlic salt.
Bake in the oven for 15 minutes or until the dough is cooked through and cheese is golden brown.
Remove from heat, let rest for a few minutes before serving.