Bresaola Carpaccio with Gribiche Vinaigrette

1/2 cup minced radish es (about 4)

2 tablespoons drained caper s (in brine), rinsed and chopped

2 tablespoons minced cornichon s or pickles (not sweet)

2 tablespoons chopped fresh chives

1 

1/2 tablespoons fresh lemon juice

1/2 teaspoon salt , or to taste

1/4 teaspoon black pepper , or to taste

3 tablespoons extra-virgin olive oil

10 ounces thinly sliced air-dried beef such as bresaola or Bundnerfleisch, or prosciutto

5 ounces baby arugula (7 cups packed)

2 tablespoons finely grated Parmigiano -Reggiano