Bring 2 quarts water to boil in large saucepan. Add cauliflower and 1 tablespoon salt and cook until florets begin to soften, about 3 minutes. Drain florets and transfer to paper towel-lined baking sheet.
Combine ½ cup hot water and saffron in bowl; set aside.
Heat oil and garlic in small saucepan over medium-low heat until fragrant and beginning to sizzle but not brown, 4 to 6 minutes. Stir in sugar, paprika, and rosemary and cook until fragrant, about 10 seconds. Off heat, stir in saffron mixture, vinegar, 1 ½ teaspoons salt, and ¼ teaspoon pepper.
Combine florets, saffron mixture, chickpeas, and lemon in large bowl. Cover and refrigerate, stirring occasionally, for at least 4 hours or up to 3 days. To serve, discard rosemary sprigs, transfer cauliflower and chickpeas to serving bowl with slotted spoon, and sprinkle with parsley.
