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 the 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. Add 1/2 cup stock, the wine, vinegar, thyme, and allspice. Cook over medium-high, 5 minutes. Add the cherries and honey and simmer for 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.