Heat 1 inch of vegetable oil in a 10- to 12-inch heavy skillet until thermometer registers 350°F, then fry tortilla strips, a handful at a time, until golden, 30 to 45 seconds.
Transfer with a slotted spoon to paper towels to drain and season with salt.
Whisk together vinegar, salt, and pepper in a small bowl, then add olive oil in a stream, whisking until combined well.
Toss watercress with dressing in a large bowl and divide among 8 plates. Divide tomatoes and tortilla strips among salads, tucking strips into greens decoratively, and sprinkle salads with cheese.
* Available at Latino markets and, in the winter months, Kitchen/Market (888-468-4433).
