Preheat oven to 425 degrees F. To roast chile peppers, halve peppers lengthwise; remove stems, seeds, and membranes. Place pepper halves, cut sides down, on a foil-lined baking sheet. Roast for 20 to 25 minutes or until peppers are charred and very tender. Wrap peppers in the foil and let stand about 20 minutes or until cool enough to handle. Use a sharp knife to loosen edges of the skins;, gently pull off the skins in strips and discard. Chop roasted peppers.
In a large bowl combine egg, bread crumbs, carrot, the water, oregano, garlic, salt, black pepper, and roasted peppers. Add ground beef; mix well. Shape mixture into four 3/4-inch-thick patties.
For a charcoal grill, place patties on the rack of an uncovered grill directly over medium coals. Grill for 14 to 18 minutes or until done (160 degrees F), turning once halfway through grilling. Toast kaiser rolls on the grill. (For a gas grill, preheat grill. Reduce heat to medium. Place patties, then kaiser rolls on grill rack over heat. Cover and grill as directed.)
Serve burgers on rolls with tomato and, if desired, avocado dip.