Heat oil in a medium skillet over medium until melted. Add chile, ginger, and garlic and cook, stirring often, until garlic has softened but not taken on any color, about 3 minutes. Add cardamom, coriander, and turmeric and cook, stirring, until fragrant, about 30 seconds. Add tomatoes and cook, stirring occasionally, until most of the tomatoes have burst and released their liquid, 12–15 minutes. Stir in coconut cream; taste and season curry with salt.
Reduce heat to medium-low. Season cod with salt and nestle into curry. Cover and cook at a bare simmer until fish is opaque throughout and beginning to flake, 5–7 minutes (thicker pieces will take longer to cook).
Gently transfer cod to shallow bowls. Stir basil into tomato curry, then spoon over fish.