Whisk together the olive oil, lemon juice, vinegar, mustard, hoisin sauce, and a pinch of salt and pepper in a small bowl. Set aside.
Heat a little olive oil in a skillet over medium-high heat. Add the baby calamari and sauté for about 2–3 minutes, just until tender. Season with salt and pepper. Remove from heat.
In a large bowl, combine the salad greens, carrots, cucumber, red onion, olives, and parsley. Add the cooked calamari on top.
Drizzle with the citrus vinaigrette, toss gently, and serve right away.