Roast the poblano peppers whole over a hot grill, under a broiler or on a gas stove flame, turning frequently until evenly blackened. Place in a bowl when done, and cover. Leave them to sweat for about 10 minutes to loosen the burnt skin. When cool enough to handle, peel the skin off by rubbing with your hands, leaving the chilies intact. Rinse off the peppers. Cut a slit down one side and open to remove the seeds and stem. Set aside.
Bring a large pot of water to a rolling boil. Add the lobster tails and cook for about 10 minutes, until bright red. Drain and cool slightly. Cut the shell lenghtwise and remove the tail meat in one piece. Set aside.
Melt 2 tablespoons of the butter in a skillet over medium heat. Add onion and garlic; cook and stir until tender and golden.
Slit the lobster tails lengthwise about halfway through. Fill the pocket with sauteed onion and garlic. Wrap each tail in one of the peppers so that the openings do not match up. Dip in egg to seal.
Heat the remaining butter in the same skillet over medium-high heat. Place the stuffed peppers in the pan with the seam side down to seal. Fry on each side just until golden. Serve immediately.
