In a blender or small food processor, combine the half peach, the onion, vinegar, oil, mustard, honey, and salt & pepper. Cover and blend or process until smooth, adding a little water if needed to thin to a dressing consistency. Taste and adjust; this should be a bit tart to balance out the sweetness of the peaches or if the peaches are very tart, make the dressing a little sweeter.
On a platter, arrange greens, and top with remaining peach slices, radishes, bacon, and Feta, along with shredded chicken if using. Drizzle with a little dressing and pass the rest on the side.
Note: this makes enough dressing to double the salad or to have enough for another salad, later. The full amount is included in the nutritional facts.