Preheat the oven to 350 degrees F. Line a sheet pan with parchment paper.
In a small bowl, whisk together the egg and water. Dip the goat cheese rounds into the egg mixture and then into the pistachios, coating them with nuts on all sides. Place the goat cheese on the prepared sheet pan and bake for 10 minutes. Cool for 15 minutes.
While the goat cheese rounds are baking, make the vinaigrette. In a small bowl, combine the shallots, white balsamic vinegar, salt and pepper. Whisk in the olive oil until fully combined.
Combine the greens, red onions, chives and strawberries and drizzle with the balsamic vinaigrette.