In a Dutch oven, simmer the squirrels in chicken broth until tender, about 2 hours. Or you can choose to cook them overnight or all day while you are at work in a Crock Pot. Pull all the meat off the bones and shred. Set meat aside and reserve the broth.
Preheat oven to 400 degrees F.
In a large skillet, boil salted water and cook gnocchi according to package directions (usually only 2 minutes). Drain water and set gnocchi aside.
Put breadsticks on a rimmed baking sheet and bake in the preheated oven for 10 minutes.
Meanwhile, in same large skillet, melt 2 Tablespoons butter over medium heat. Add chopped onion and cook, stirring frequently for 2 minutes. Stir in garlic and thyme and cook another 1 minute.
Add another 2 Tablespoons butter and whisk in flour until lightly browned, about 2 minutes.
Gradually add reserved chicken broth, and cook, whisking constantly until thickened, about 3 minutes.
Stir in gnocchi, kale, squirrel meat, half and half, and Sazon seasoning packet. Serve immediately with a sprinkle of grated Parmesan and warm breadsticks.