Puree 4 strawberries and onion (or scallion) in a small food processor or blender until chopped. Add garlic, vinegar, oil, tarragon, mustard, salt and pepper; pulse until well combined. Taste and add a little agave (or sugar) if the dressing is too tart.
Toss arugula and feta in a large bowl. Slice the remaining strawberries and add to the bowl. Toss the salad with the dressing.