In small bowl, whisk together olive oil, vinegar, shallot, garlic, salt, pepper and sugar.
Working with one pepper at a time, cut in half lengthwise. Open up each half and lay flat in single layer on large platter. Repeat with remaining peppers.
Arrange anchovies in pleasing pattern on top of peppers. Roughly chop eggs and arrange over peppers and anchovies. Spoon vinaigrette over and sprinkle with parsley. Serve with toast.
Notes
A Spanish Arbequina oil is our preferred choice – it’s light, grassy and not at all bitter or peppery like some other olive oils.