Using a blender or food processor, pulse jalapeño with zest, vinegar, pepper, sugar and 1 1/2 teaspoons salt until JUST chopped. Blend in the olive oil.
In a medium saucepan, heat 1" of oil to 350°. Fry tortilla strips until crisp and golden, about 1 minute. Drain on paper towels and season with salt. Alternatively, preheat oven to 400°. Spread tortilla strips on sheet and spray with oil. Sprinkle salt and bake for 8 minutes, until golden and crisp.
In a large mixing bowl, toss greens with vinaigrette. Mound salad on chilled plates and top with cheese and tortilla strips.