Preheat oven to 425F and line a large sheet pan with parchment paper.
Make the dressing: Whisk or shake all ingredients – water, olive oil, lemon juice, lemon zest, garlic, oregano, black pepper, and salt – in a small bowl or jar vigorously to combine and set aside.
Add the chicken pieces to a large bowl. Pour in half of the dressing (about ⅓ cup) and mix to coat the chicken. Cover and refrigerate for at least 20 minutes (or up to 2 hours) to marinate.
Meanwhile, make the salad: Add the spinach, peas, and green onions to a large bowl. Add the remaining half (about ⅓ cup) of the dressing and toss gently to coat. Cover and chill until serving.
When the chicken is done marinating, fill eight 8-inch metal skewers with chicken pieces, about 4 to 6 pieces per skewer depending on the size (see notes if you do not have skewers). Bake, flipping halfway through, until light browned on the outside, 20 to 22 minutes. Turn the broiler to high and broil for an additional 5 to 7 minutes to get crispy outsides.
Divide the salad between 4 plates and place 2 skewers on each.
