Pulse the dried roasted peppers, mayonnaise, balsamic and pepper in a small processor until smooth. Scrape into a bowl and refrigerate while preparing the bread.
Split each mini croissant horizontally without crushing its top. Divide mortadella and Fontina into 24 equal portions.
Spread the pepper mayonnaise thinly over the cut faces. Put a few dry arugula leaves on each bottom and fold one portion of mortadella over the leaves.
Add one portion of Fontina and close each croissant gently. Keep the filling within the edges so the sandwiches can be picked up easily.
Arrange in a single layer in a covered shallow container and refrigerate until serving, preferably within 4 hours. Yield 24 whole mini sandwiches, two per serving.