In a large heavy-based pot or dutch oven, heat butter and fry leek over medium low heat for 5 mins or until soft. Add garlic and fry for 30 seconds.
Add flour to butter/leek mixture in pot and cook, stirring for 2-3 mins or until butter/flour mixture becomes grainy and frothy. Remove from heat.
Add stock to flour mixture gradually (about ¼ cup at a time) making sure that stock is fully incorporated and mixture is lump free before each new addition. Once this process is finished, mix in milk & grated carrot and bring to a simmer.
Simmer for 5 mins, or until carrot is almost cooked when tested.
Then add chicken, spinach & gnocchi (uncooked) to pot and mix to combine. Bring to a simmer, and continue to simmer until gnocchi is tender and cooked - this should only be a few minutes once simmering.
Taste test for salt and pepper, then serve with fresh grated parmesan.