Pat shrimp dry and season lightly with salt and pepper.
Warm the coconut oil in a large skillet over medium heat.
Sauté onion and bell pepper until softened, about 4 to 5 minutes.
Stir in garlic and ginger; cook until fragrant, about 30 seconds.
Bloom the red curry paste in the pan for 1 minute, stirring.
Pour in crushed tomatoes and broth; scrape the pan and simmer 3 minutes.
Stir in coconut milk, fish sauce, and brown sugar; bring to a gentle simmer.
Add shrimp and cook, stirring, until pink and opaque, 3 to 4 minutes.
Turn off heat; stir in lime juice and most of the cilantro. Adjust salt.
Serve hot, topped with remaining cilantro and a pinch of red pepper flakes.