Preheat oven to 375 degrees. Rub peppers with 2 teaspoons olive oil. Place them on a baking sheet and roast for 25 minutes or until almost charred. Remove and place in plastic container with a lid to steam and cool. When cool enough to handle, push off the skins and remove stems and seeds. Place peppers in food processor fitted with metal blade and puree along with the vinegar, 1 teaspoon olive oil, and 1 tablespoon water. Season to taste.
Wash asparagus. with a sharp knife, trim bottoms to make spears of equal length. Place the asparagus in boiling water for 1 minute. Drain and refresh. Pat dry. Toss with 2 teaspoons olive oil. Cut the ham in half lengthwise.
Hold 3 asparagus spears together. Wrap one strip of ham around the center of the asparagus bundle and set aside. Continue making bundles until you have 12.
Carefully lay one sheet of phyllo dough on damp towel. Lightly brush it with some of the melted butter and sprinkle with 1 tablespoon bread crumbs. Butter another sheet and place on top of the crumbled sheet. Using a very sharp knife, carefully cut the phyllo sheets, from top to bottom, into 6 strips. Roll one phyllo strip around the center of an asparagus-ham bundle. continue until you have prepared 6 bundles. Repeat the process with the remaining phyllo sheets, butter, crumbs, and 6 remaining asparagus bundles. Place bundles on baking sheet . Bake for 9 to 12 minutes, or until pastry is golden brown.
Toss arugula leaves with remaining teaspoon of oil. Place a tablespoon or more of pepper puree in center of each plate. Cross 2 asparagus bundles over the puree. Garnish with a few arugula leaves and serve immediately.