In a large heavy skillet cook the onion, garlic, cumin, and chili powder in 1 1/2 tablespoons of oil over moderately low heat, stirring, until the onion is soft. Add the beef, and cook the mixture over moderate heat, stirring and breaking up any lumps, until the meat is no longer pink. Add the tomato paste and salt and pepper to taste and cook the mixture, stirring, until the meat is cooked through. Transfer the mixture to a bowl and let it cool.

In the skillet, cleaned, heat 3/4-inch of the additional oil to 375F (190C) and in it fry the tortilla chips in batches for 30 seconds to 1 minute, or until most of the bubbling subsides. Transfer the chips with a slotted spoon to paper towels to drain and sprinkle them with salt to taste. The tortilla chips may be made 1 day in advance and kept in an airtight container.

On a large deep platter or in a large bowl arrange the romaine, spoon the beef mixture over it, and arrange the tortilla chips, tomatoes, Cheddar, and scallion decoratively over the salad.

Make the vinaigrette: In a blender blend together the garlic, vinegar, lemon juice, cumin, and salt and black pepper to taste, with the motor running add the oil in a stream, and blend the vinaigrette until it is emulsified. Add the tomato, the jalapeno pepper, and the cilantro and blend the vinaigrette until it is smooth. Transfer the vinaigrette to a small bowl and serve it with the salad or pour the vinaigrette over the salad and toss the salad until it is combined.