Thinly slice all of the strawberries. Set aside 3 large berries for the dressing.
Make the dressing. In the bowl of a food processor or a high-speed blender, add the 3 reserved strawberries, oil, vinegar, Dijon, shallot, water, and honey. Process until smooth and creamy, adding more water if necessary. Season with salt and pepper to taste.
On a large serving platter or in a large serving bowl, mix the arugula, strawberries, pecans, basil, and feta. Drizzle with vinaigrette and serve immediately.
