This is a soup rarely heard about today but was quite common in the 19th Century even into the 20th Century. In a way it makes sense that it is called Scotch Broth since lamb or mutton is the primary source for the soup. Most of the recipes I found were very similar so I'm only putting a select few for today's post.
Take about eight pounds of the neck and bone parts of lamb or mutton. Trim off all the outside or skin parts. Cut off the lean portion (being careful not to take any fat), cut in small bits and save for the next day. Put to boil all the trimmed parts. Boil several hours, strain and keep until next day. Remove all the fat, add one-half cupful of pearl barley, cook four hours. Add two onions, one-half carrot and one turnip chopped fine. .Also cook the small bits of meat and add to the broth. Season to taste with salt, pepper and parsley chopped fine.—Lyda McKinley.
The Puritan Cook-Book ©1898
Scotch Broth.—Cut the neck mutton into chops and put it in a saucepan with 4 pints of water, as soon as it boils taie off the scum, and then add 2 turnips cut in small 8 squares, 1 large carrot, and 3 onions also cut, 3 tablespoonsful of mushroom ketchup. Cover it closely, and let it stew for four or five hours gently. Then take out the meat and cut it in small pieces, and after skimming all the fat from the broth return the meat to it, season it and send it to table with the addition of a small quantity of light dumplings the size of a walnut or suet dumpling.
Source: Tried & Approved Recipes ©1878
Scotch. Broth.—Take some middle cutlets from neck of mutton; trim them ; then take the trimmings and put them into a stewpan, with some of the scraps and small pieces of knuckle of veal; moisten well with good boiling broth, and season with some sticks of celery, leeks, parsley, a very large onion stuck with two cloves, a few slices of turnip cut into dice, and one or two carrots also cut into dice. Let this broth boil gently for three hours, season with salt and pepper, and skim off the fat. When it becomes a good flavour drain it over the chops, which must be put in a large enough stewpan to contain the soup. Have some well-washed barley which has been boiling for a long time, and put it into the soup with the chops to boil for one hour. Skim before sending to table. Chop a little parsley very fine and add just before serving.
Source: Housewife's Referee ©1898