Soften the red onion. Heat 2 teaspoons of olive oil in a 10-inch (26 cm) skillet over medium-low heat. Add the red onion cut into thin circles and cook for 3 to 4 minutes, until softened and lightly golden. Push the onion to the edge of the pan.
Season and toss the chickpeas. Add the cumin, thyme, hot paprika and salt to the empty center of the pan. Add the very dry chickpeas and toss them on the hot pan for 5 to 7 minutes, until heated through and lightly golden. Keep the heat at medium or medium-low so the paprika doesn’t burn. Move everything to a bowl.
Slice the vegetables. Cut the carrot into very fine rounds or small pieces. A mandoline gives the best, most delicate effect. Halve the cherry tomatoes and slice the pear thinly. Add the carrots to the warm chickpeas and onions so they soak up the aroma of the spices. If you cut the carrots thicker, roast them in the pan together with the chickpeas for a few minutes so they stay crisp but are not hard.
Blend the pink dressing. Blend the cooked beetroot, Greek yogurt, apple cider vinegar, olive oil and salt until completely smooth. Add water 1 teaspoon at a time until the dressing is creamy and easy to drizzle. Taste and adjust the salt or vinegar. If you like it sweeter, add a small drizzle of honey or maple syrup, to your taste. Discover how to easily bake beets in foil with my foolproof, step-by-step recipe: Easy Oven Roasted Beets in Foil. Arrange the salad. Break the romaine into pieces. Fan the nice outer leaves around the edge of each plate and place the rest in the center, then top with arugula. Add the chickpeas with onions and carrots. Cut the mozzarella into rounds, then tear them with your hands into smaller pieces. Scatter the mozzarella and halved tomatoes over the top and fan the pear slices on one side.
Finish and serve. Spoon the pink dressing over the salad in circles or thin ribbons just before serving. Sprinkle with chopped walnuts and fresh parsley.