Brown the chops in a pan with the olive oil, about 5 - 7 minutes on the first side, 3- 5 on the second side until nicely browned. Remove from the pan and keep warm.
Add a bit more olive oil to the pan and toss in the steamed Brussels Sprouts. Let them cook for a few minutes until they start to brown, then add in the apples and cook for about 5 more minutes until the apples soften. Add the shallots and stir the mixture around until the shallots start to color and soften. Add in the white wine or broth and deglaze the pan briefly. Add in the balsamic vinegar, tossing it into the ingredients so it gets evenly distributed.
Add the chops back into the pan, nestling them in among the apples, brussels sprouts and shallots. Cover and cook over a medium to low heat until the chops are cooked through, about ten more minutes. Add a bit more white wine or broth if the pan seems too dry.
To serve, arrange a bed of brussels sprouts, apples and shallots on each plate, top with a chop and drizzle the pan juices over all.