Dry the fillets with paper towels and sprinkle with salt and pepper on both sides. Heat the oil medium-high in a skillet large enough to hold the meat in a single layer. If your pan is smaller, do two batches.
When the pan is hot, lay the pieces in the pan—don’t crowd. Sauté about two minutes, until the meat is nicely browned, then flip and cook on the other side, another two minutes.
Remove the veal to a plate and keep warm. Sauté any remaining pieces and reserve on plate with others when done.
Return the skillet to medium high. Add the capers to the pan and let them cook for about 30 seconds, then add the vermouth to deglaze. Scrape up any brown bits on the bottom of the pan—they’re pure flavor. This won’t take long. Cook the pan sauce until the wine is reduced by about half, about two minutes, then add lemon juice and stir.
Add the butter bit by bit to enrich the sauce,taste and reseason if needed. Place the veal back in the pan, add the lemon peel, and stir to let the sauce coat the meat. Sprinkle parsley on top and serve.