Butter a half-sheet pan (about 12 by 17 inches), line it with parchment paper, and butter the parchment paper. Set aside.
Bring the broth, salt, white pepper, and cayenne to a boil in a medium saucepan over high heat. With broth mixture at a boil, gradually pour in the grits, while whisking constantly. After the grits are incorporated, reduce heat to a simmer, and cook, stirring constantly, until the grits are thick, about 5 minutes. Add the cheese and stir until melted. Spread the grits in an even layer about 1/2-inch thick in the prepared pan and refrigerate until set and firm, at least 1 hour.
Bring the smoked turkey stock to a boil in a medium saucepan over high heat. Add the greens and adjust the heat to maintain a simmer. Cook, stirring occasionally, until greens are tender and liquid has evaporated, about 1 hour. Remove from heat and add the cider vinegar. Keep warm while frying the grits cakes.
When the grits are set and firm, turn the grits out onto a clean cutting board. Using a 1 1/2-inch round or square cutter, cut the grits into small cakes. Put some instant flour on a plate and season with salt and pepper, to taste. Dredge the cakes in the seasoned flour. Heat the olive oil in a large skillet, and fry the cakes, in batches, until golden brown, about 3 to 4 minutes per side. Remove from the pan and drain on a paper towel-lined plate.
Top each grits cake with some of the braised greens and serve.
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Bring 3 quarts of water to a boil in a large pot. Add all the ingredients, reduce heat, and simmer for 1 hour. Strain the broth into a large bowl or plastic container. If not using immediately, fill the sink up with ice water to come about halfway up the sides of the container. Nestle the broth in the ice bath and stir it periodically to cool it down. Cover and refrigerate for up to 5 days or freeze for up to 3 months.
Yield: approximately 2 1/2 quarts