- 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. Set grilled corn aside.
- Cut kernels off 3 remaining ears of corn. Once cooled, do the same with grilled corn, keeping corn kernels in separate bowls. Reserve cobs.
- Using coarse side of box grater, grate any milky juices from the reserved cobs into medium bowl.
- Melt 1 tablespoon butter in large saucepan over medium heat. Add Tasso ham and sauté until almost crisp, approximately 4–5 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, 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 quite thick and mixture has very little liquid.
- Season with salt and pepper. Sprinkle with green onions and toasted cornbread crumbs
and serve warm.