In a jar or salad bottle with a tight-fitting lid, combine olive oil, lime juice, champagne vinegar, thyme, shallot, and Serrano pepper. Shake well.
Season dressing with salt to taste; chill in refrigerator.
Meanwhile, slice watermelon into 3″ squares, about ¼-inch thick.
On small salad plates, begin to assemble each serving of the salad.
To assemble, place one slice of watermelon on the plate; next, layer one slice of feta on top of the first watermelon slice. Repeat, layering another watermelon slice and then one more feta slice. End with a final watermelon slice on top.
Place about one handful of arugula on the plate, encircling the stacked watermelon/feta. Drizzle the stack and the arugula with the vinaigrette and garnish with a few slices of Serrano pepper.