Brush corn with 2 tablespoons vegetable oil and grill over medium-high heat, turning occasionally until corn is slightly charred. Let cool several minutes then remove corn from cobs and set aside.
In a large skillet over medium-high heat, heat remaining 1 tablespoon oil until shimmery. Add zucchini and onion and saute several minutes until slightly softened. Add garlic, curry paste, turmeric, and cayenne and saute 1 additional minute until fragrant.
Reduce heat to medium and stir in tomato paste, charred corn, crushed tomatoes, and coconut milk stirring until combined. Bring curry to a low simmer over medium heat, then reduce heat to low and let simmer 15-20 minutes to develop flavors.
Season curry with salt and pepper to taste. Serve curry hot over rice with cilantro and fresh lime juice over top and enjoy!
Storing InstructionsStore curry in refrigerator up to 6 days.