1 Heat ¼ cup of oil in a large sauté pan over medium-high heat. Using tongs and working in batches, fry the pastrami in a single layer until crisp and deep dark red, almost blackened, about 7 to 9 minutes. Drain on paper towels, and let cool slightly.
2 Pour balsamic vinegar into a skillet that has preheated for a couple of minutes over medium-high heat.
3 Bring the vinegar to a boil, then reduce the heat to medium and allow it to simmer, thicken and reduce. Stir or whisk the vinegar occasionally as it simmers to prevent burning.
4 Remove the pan from the heat when the vinegar has reduced to about 1/3 of a cup and is syrupy. Allow the vinegar to sit a few minutes more; it will continue to thicken.
5 Toss the greens with the remaining 3 tablespoons of olive oil in a large salad bowl. Crumble the pastrami into bits by hand or chop with a knife. Top the salad with the pastrami-fry. Drizzle with balsamic reduction and salt and pepper to taste. Serve any extra pastrami-fry in a dish on the side so people can add more if desired.