Melt 2 tablespoons butter in a large nonstick skillet over medium-high heat. Add the poblanos and bell pepper and cook, stirring occasionally, until tender and browned in spots, about 5 minutes. Add the scallion whites, thyme, 1 teaspoon salt and a few grinds of pepper and cook, stirring, until the scallions are tender, 1 to 2 minutes. Set aside to cool slightly.
Make the custard: Whisk the eggs, chicken broth, half-and-half, 1 teaspoon salt and a few grinds of pepper in a large bowl. Add the creamed corn, bread cubes, 2 cups cheese, the scallion greens and poblano mixture; toss gently until combined. Let sit until the bread is soaked, at least 30 minutes.
Preheat the oven to 350˚. Butter a 3-quart baking dish. Transfer the stuffing to the prepared dish. Sprinkle with the remaining 1/2 cup cheese and dot with the remaining 2 tablespoons butter.
Bake the stuffing until the custard is set and the top is browned, about 1 hour. Let cool at least 20 minutes before serving.