Prepare the Tomato Basil Vinaigrette: Add all ingredients to a food processor and process until chopped and well combined. Taste, add salt and pepper and adjust as necessary, adding more olive oil if needed. (This vinaigrette is should not be overly acidic, so the flavours of the basil, tomato and jalapeno aren't over-powered.) Place into a jar and refrigerate until needed.
Prepare the Salad: In a large bowl, combine all the ingredients. Drizzle with some of the Tomato Basil Vinaigrette and toss well to coat. Garnish with freshly shaved Parmesan cheese and salt and pepper, to taste.