Heat olive oil and butter in a large pot over medium heat until melted and slightly foamy. The base should smell rich and buttery.
Add onion, celery, and garlic, then cook for 3–4 minutes until soft and fragrant but not browned. The vegetables should look slightly glossy.
Crush rosemary, thyme, fennel seed, celery seed, pepper, and red pepper flakes lightly. Stir them into the pot so the aroma blooms quickly.
Add chicken broth, clam juice, and tomato paste, then stir until the broth turns a deep reddish-orange color.
Bring to a gentle simmer, then reduce heat and cook uncovered for 60–75 minutes. The broth should smell deeply herbal and slightly spicy.
Stir in white wine or beer and let it simmer for another 15–20 minutes to deepen the flavor. The broth should look slightly richer and darker.
Taste and adjust salt if needed, keeping the broth balanced but flavorful.
Add shrimp and cook for 2–3 minutes until pink, curled, and opaque. Do not overcook or they will turn rubbery.
Remove from heat immediately and let it rest for 1–2 minutes before serving.
Ladle hot broth and shrimp into bowls and serve with crusty bread for dipping.