Heat 1 tablespoon oil in a skillet over medium heat. Add shallots and sauté until golden and crispy. Remove and set aside.
In the same skillet, heat another tablespoon of oil. Stir in red curry paste and tomato paste; cook for 1 minute.
Add coconut milk, fish sauce, soy sauce, brown sugar, ginger, turmeric, and salt. Simmer for 5–10 minutes.
Add shrimp and simmer until pink and cooked through, about 3–5 minutes.
Squeeze in lime juice. Serve curry over rice and top with crispy shallots and herbs.