For the grits: In a large pot over medium heat, cook the bacon and onions until the bacon is chewy and the onions are translucent, about 1 minute. Pour in the grits and add the chicken broth. Stir together and bring to a boil. Reduce to a simmer, cover and cook, stirring occasionally, for 30 to 40 minutes. Add the cream and cayenne, stirring them into the grits. Cover the pot and keep cooking over very low heat, stirring occasionally to keep them from sticking, until the grits are tender but still have a bite to them, another 20 to 30 minutes.
Just before serving, stir in the cheese. Add salt and pepper to taste.
For the pork chops: Melt the butter with the oil in a large skillet over medium-high heat. Sprinkle the pork chops on both sides with salt and pepper. Add the pork chops to the skillet and cook until golden brown, about 2 minutes per side. (They'll finish cooking in the skillet later.) Remove the pork chops to a plate.
Put the skillet back on the heat, add the Applesauce and pour in the wine and vinegar. Cook until the liquid reduces by half, about 5 minutes. Pour in the maple syrup, stir it in and allow it to come to a bubble. Add the pork chops to the skillet, reduce the heat to low, cover and cook for another 20 minutes.
To serve, spoon a generous helping of grits onto a plate. Lay a pork chop on top of the grits, and then spoon the apples over the top. Be sure to get a little extra pan sauce onto the plate.
Throw the apples, apple juice and lemon juice into a pan and bring it to the boil over medium-high heat. Lower the heat and simmer until the apples are soft, about 15 minutes. Stir through the sugar and mix until melted. Add the cinnamon and stir through.
Puree the mixture in a food processor, blender or food mill. If not using right away, leave to cool and then refrigerate.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.