In a large soup pot, over medium-high, melt butter, or heat the oil until shimmering.
Add carrot, celery and onion; cook, stirring occasionally, until lightly browned at the edges; 7 to 10 minutes.
Stir in garlic and sage; sauté for a minute, until fragrant.
Stir in salt, pepper, nutmeg and cayenne.
Tie the thyme and parsley sprigs and the bay leaf together with a piece of kitchen twine to make a bouquet garni; add to the pot (or just throw the herbs directly into the pot; you’ll just have to fish them out later).
Add stock and barley; bring to a boil.
Reduce to a simmer and cook until barley is almost done; about 30 minutes.
Add turkey and cook until barley is tender; about 10 to 15 minutes longer.
Remove from heat and remove the bouquet garni or individual herbs.
Squeeze the juice from half a lemon into the soup; stir in chopped parsley.
Taste and add more salt, pepper and lemon juice, if you like.
Cut the remaining lemon half into wedges.
Garnish soup with more parsley and serve with lemon wedges.
