In food processor, combine garlic, chili pepper, ginger, cilantro, lime zest and olive oil. Process to a paste and transfer to a large bowl.
Whisk in coconut milk and lime juice. Season with salt.
Bring a pot of water to a boil over high heat, about 7 minutes. Add mussels, tomatoes, and bell peppers. Cover and cook. Shake the pot a few times, until the mussels just begin to open, about 4 minutes.
Uncover the mussels and stir in coconut milk mixture. Cover and cook, shaking the pot a few times, until all of the mussels open, for about 8 minutes.
Spoon mussels and broth into a bowl and serve. Season to taste.