- Brush 3 ears corn with oil and sprinkle with coarse salt, black pepper, and cayenne pepper. Grill corn until cooked through and slightly charred, turning occasionally, about 10 minutes. Let cool.
- Cut kernels off remaining 3 ears of corn. Repeat with grilled corn when cooled, keeping corn kernels in separate bowls. Reserve cobs.
- Using the coarse side of a box grater, grate any milky juices from the reserved cobs into a medium bowl.
- In a large saucepan over medium heat, melt butter. Add Tasso ham and sauté until almost crisp, approximately 4 to 5 minutes. Add shallots, poblano or jalapeño, onion, green tomato, red pepper, thyme, and garlic. Sauté until onion is translucent, about 4 minutes. Add uncooked corn kernels and sauté 3 minutes. Next, add corn juices and grilled corn. Cover, reduce heat to low, and simmer 8 minutes. Mix in 2 tablespoons butter, then add heavy cream. Simmer until thick and mixture has very little liquid. Season with salt and pepper. Sprinkle with green onions and toasted cornbread crumbs and serve warm.