Bring a large pot of salted water to a boil. Cook the pasta according to the package instructions until al dente. Reserve half a cup of pasta water, then drain and keep the pasta warm.
Dice the smoked turkey into bite-sized pieces. Slice the andouille sausage.
Separate the kale leaves from the stems and tear them into smaller pieces. Rinse under cold, running water and let drain. Set aside.
In a large skillet, heat a tablespoon of oil over medium-high heat. Once hot, add the shredded turkey and sliced andouille sausage with one tablespoon Cajun seasoning, salt and pepper. Cook for about five minutes or until the sausage begins to brown. Remove the meat from the pan and set aside.
Using the same skillet, saute the onions in the remaining avocado oil over medium heat for about two minutes. Add the chopped kale to the skillet and sauté until wilted, about 4-5 minutes. Add the garlic and cook for another 30-60 seconds until fragrant. Then, add the diced tomatoes and saute for an additional two minutes.
Pour in the heavy whipping cream, chicken broth, remaining Cajun seasoning, and parmesan cheese. Bring the mixture to a simmer and season to taste if needed.
Add the shredded turkey and cooked pasta to the sauce and toss until well combined. Add reserved pasta water, if desired, to thin out the sauce. Serve with freshly grated parmesan, green onions or chopped parsley.