In a large saucepan, combine the beef, sliced onion, whole garlic, 1 teaspoon salt, and enough water to cover. Bring to a boil, lower the heat, and simmer, covered partially, until the beef is tender, about 1 1/2 to 2 hours. Let the beef cool in the broth and drain it, reserving 1/3 cup of the broth. Using 2 forks, shred the beef and set aside.
Heat the oil in a large skillet over moderately low heat. Cook the minced onion and garlic, stirring occasionally, until softened. Add the beef, tomato sauce, chile, cumin, reserved broth, and salt and pepper, and simmer, stirring, until thickened, about 3 to 5 minutes. Let the beef filling cool.
Working with 1 warmed tortilla at a time, and keeping the others covered with a kitchen towel, spread about 2 rounded tablespoons of the filling down the center of each tortilla, roll up the tortillas, enclosing the filling, and secure the ends closed with wooden picks. Keep the rolled tortillas covered with plastic wrap. The flautas may be prepared up to this point 2 hours in advance and kept covered tightly with plastic wrap and chilled.
Pour enough oil into a straight-sided skillet to reach about 1/2-inch up the sides. Heat the oil over moderately high heat until it is hot but not smoking. Fry the flautas in batches, turning them, until crisp, about 2 minutes. Transfer them with tongs to a paper towel-lined plate to drain. Spread the lettuce on a platter or divide it among 6 plates, arrange the flautas on it, and top them with guacamole, sour cream, and salsa.
Cook's Note: To warm tortillas in the oven: Stack 6 tortillas at a time, wrap each stack in foil, and heat the tortillas in the middle of a preheated 325 degrees F. oven for 5 minutes. (If the tortillas are very dry to begin with, pat each tortilla between dampened hands before stacking them.) Alternatively, to warm them in a microwave oven: Stack 6 tortillas at a time, wrap each stack in a microwave-safe plastic bag, and heat in a microwave oven at high power for 30 seconds to 1 minute, or until they are heated through and pliable.
Recipe courtesy of Gourmet Magazine