Preheat oven to 230°C (450°F). In a bowl, toss asparagus, onion, celery, and garlic with olive oil. Season to taste with salt and pepper.
Place vegetables on a parchment-lined baking sheet and roast, uncovered, until just beginning to brown, about 10 minutes. Shake pan once during cooking to turn vegetables.
Transfer vegetables to a medium saucepan over medium-high heat. Stir in flour; then stir in broth. Bring to a boil, reduce heat, and simmer for 10 minutes. Carefully pour into a blender and purée until smooth. Return to saucepan and heat through.
When ready to serve, spoon 15 mL (1 tbsp.) of tzatziki over each serving and sprinkle with freshly ground pepper.