Heat the olive in a large saucepan or Dutch oven over a medium heat. Add the pancetta and cook through until golden brown. Remove from the pan with a slotted spoon and set to one side.
Thinly slice the shallot and garlic and finely chop the rosemary. Add the shallot, garlic, rosemary, and thyme to the Dutch oven/saucepan used to cook the pancetta. Add the butter. Sweat gently over a low/medium heat for a few minutes until tender and fragrant.
Add the stock and bring to a gentle boil. You may use an alternative stock if preferred, such as vegetable. You may also add salt and pepper if desired. This will depend on the strength of seasoning already in your stock. Reduce the stock to a simmer for five minutes.
Roughly shred the cooked turkey into bite-sized chunks. Cut the tough bases from the sprouts and remove any tough or wilted outer leaves. Add the Brussels sprouts and shredded turkey to the stock. Simmer for 5/6 minutes to heat the turkey through and cook the sprouts.
Add the kale to the saucepan and stir to combine. Simmer for a minute or two until the kale has just wilted. The turkey should be piping hot through.
Divide the soup between four serving bowls. Top each bowl with a scattering of the crispy pancetta. Drizzle each bowl with 1/2 a tablespoon of olive oil to serve.