Put oven rack in middle position and preheat oven to 325°F.
Arrange salami slices in 1 layer on a large baking sheet lined with parchment paper. Bake until edges are crisp and beginning to curl, 10 to 12 minutes.
Transfer salami to a rack to cool, arranging it in 1 layer. (Slices will crisp as they cool.) Leave oven on and discard parchment paper.
Arrange croissants, cut sides up, on same baking sheet and toast in oven until just golden, 3 to 5 minutes.
While croissants toast, whisk together eggs, milk, cream cheese, salt, and pepper until eggs are combined well (cream cheese won't blend into egg mixture completely).
Heat oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking. Pour in egg mixture and cook, scraping up cooked egg with a heatproof rubber spatula and letting raw egg run underneath, until egg is set, about 3 minutes. Season eggs with pepper.
Assemble croissant sandwiches with arugula, eggs, and crisped salami.
