In a large skillet, heat the oil over medium-high. Pat chops dry, season with salt and pepper and cook until browned, 4 minutes per side. Transfer to a plate; pour off the drippings.
In the skillet, cook the collard greens with 1 cup stock and the garlic over medium until tender, 10 to 15 minutes. Season; transfer to a bowl.
In the skillet, melt 3 tbsp. butter over medium. Add the shallot and cook, stirring often, until tender, 3 minutes. Add 1/2 cup stock, the wine, vinegar, thyme and allspice. Cook over medium-high, 5 minutes. Add the preserves and simmer 5 minutes. Stir in the remaining 2 tbsp. butter; season.
Divide the collards and pork chops among plates and top the chops with the cherry sauce.