Heat a saucepan over medium-high heat. Add 1 tablespoon of olive oil, 3/4 cup chopped onion, and 1/3 cup chopped celery; sauté 3 minutes. Add 2 cups water, 1 cup bulgur; bring to boil. Cover, reduce heat, and simmer 11 minutes. Dice plums, lightly chop spinach and parsley.
Allow bulgur to cool to room temperature. Add all ingredients together with remaining olive oil and a spritz of fresh lemon juice. Serve immediately or cover and chill. Season with salt and pepper, if desired.