Place eggplant slices on 2 baking sheets. Lightly salt eggplant on both sides. Let stand 1 hour. Drain on paper towels, pat eggplant dry, wiping off salt.
Heat oil in heavy large pot over medium-high heat. Sauté half of beef until brown, about 3 minutes. Using slotted spoon, transfer beef to bowl. Sauté remaining beef until brown, about 3 minutes. Return all beef to pot. Add salsa, broth, garlic, sugar and soy sauce; bring to boil. Reduce heat to medium-low, cover and simmer until beef is tender, stirring often, about 1 hour 10 minutes.
Uncover pot and simmer stew until sauce thickens, about 5 minutes. Mix in cilantro and lime juice. Season with salt and pepper. (Can be made 2 days ahead. Refrigerate until cold, then cover and keep refrigerated. Rewarm before continuing.)
Heat tortillas 1 at a time on stove burner, about 10 seconds per side, turning with tongs. Cover with towel to keep warm.
Serve stew with tortillas, allowing diners to assemble tacos.