Season the veal chops generously with salt and let them sit for 15 to 20 minutes.
Rub the chops with oil on both sides and arrange on the preheated grill on a very hot spot. After about 3 to 4 minutes, when the chops have developed lovely grill marks, rotate the chops 90 degrees to create the cross-hatch pattern. Cook the chops for an additional 3 to 4 minutes on that side and then repeat the process on the other side. This will cook the chops to about medium-rare. Remove the chops to a serving platter and set aside in a warm place to let the juices redistribute.
While the chops are cooking, coat a large saute pan with extra-virgin olive oil and over medium heat add the garlic cloves.
When the garlic has become golden brown and is very aromatic, remove and discard the garlic. It has fulfilled its garlic destiny. Add the potatoes, season with salt and brown the potatoes on each side. When the potatoes are brown on each side, add the mushrooms and season with salt. Saute the mushrooms for 5 to 7 minutes. When the mushrooms have become soft and aromatic, add in the cherry peppers and 2 to 3 tablespoons of the pepper vinegar (more if you like things REALLY spicy). Add the vinegar in baby steps, it can make things VERY spicy and there will not be any recovery. Check for seasoning and season with salt if needed (it will). Toss in the chives. Transfer the potato mixture to a serving bowl or platter and serve immediately with the veal chops drizzled with extra-virgin olive oil.