Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Prick the skin of the eggplants in several places and place on the baking sheet.
Broil eggplants in the preheated oven, turning occasionally, until charred on all sides and completely tender when pierced with a fork, about 20 minutes. Remove from oven and allow to cool until easy to handle, about 15 minutes. Remove eggplants' stems and peel; dice flesh.
Melt butter in a large skillet over medium-low heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes. Stir in tomatoes and cook until soft, about 5 minutes. Stir in diced eggplant, salt, and pepper. Pour eggs over vegetables and mix until scrambled and no longer runny, about 5 minutes.