For the dressing: In a bowl, combine the shallot, lemon juice, vinegar, and salt and set aside for at least 10 minutes. Stir in the oil and pepper and refrigerate the vinaigrette until you’re ready to use it, or for up to 2 days.
For the veal: Preheat the oven to 250°F. Line a baking sheet with paper towels.
Break the breadsticks into a bowl wide enough to dredge a chop and use a wooden spoon or a fork to crush them to the size of peas. (The reason I don’t use a food processor is that I don’t want the crumbs too fine.) Add the parsley and garlic and stir to combine. In a second wide, shallow bowl, whisk the eggs and milk. Pour the flour into a third wide, shallow bowl.
Working in an assembly line fashion, season the chops on both sides with salt and pepper and dredge the chops in the flour. Next, dip the chop into the egg mixture, turning to coat them evenly on both sides. Lay the chop in the breadcrumbs and gently press down to adhere the crumbs to the meat. Turn and do the same thing on the other side. Set the chop on a plate and continue breading all the chops in the same way.
Pour enough oil into a large skillet to come up 1/4 inch and heat it over high heat for about 2 minutes, until a pinch of salt sizzles when dropped into the oil. Carefully slide one chop into the oil and cook until it’s golden brown, 2 to 3 minutes per side. Transfer the chop to the baking sheet and place it in the oven while you cook the rest of the chops. (Putting them in the oven keeps them warm, but it also cooks the meat closest to the bone, which doesn’t cook through in the skillet.) Cook the remaining chops in the same way. Add more oil to the pan as necessary and make sure it’s hot before adding another chop. When you’ve cooked the last chop, put it in the oven with the others for 4 minutes to cook the meat closest to the bone.
For the salad: Put the arugula and tomatoes in a large bowl. Sprinkle the greens and tomatoes with salt and drizzle with 1/4 cup of the dressing. Toss gently and add more dressing if desired.
Remove the chops from the oven and transfer each one to a dinner plate. Squeeze a generous amount of lemon juice over each chop. Serve on top of the salad to maintain the crust.