4 ounces pepper jack cheese, shredded (1 1/4 cups)
Light a grill or preheat the broiler. Grill or broil the poblano, turning frequently, until charred all over, about 4 minutes. Transfer the chile to a bowl, cover with plastic wrap and let stand for 15 minutes. Peel and seed the poblano and cut it into 1/4-inch dice.
Preheat the oven to 350°. Lightly butter an 8-inch round cake pan. In a medium skillet, melt 1 tablespoon of the butter. Add the onion and cook over moderately high heat until softened, about 5 minutes. Add the poblano and corn and cook until heated through, about 1 minute.
In a large bowl, whisk the flour with the cornmeal, sugar, baking powder and salt. Add the 6 tablespoons of melted butter along with the milk and eggs and whisk until just incorporated. Fold in the poblano-corn mixture and 3/4 cup of the pepper jack cheese. Scrape the batter into the prepared cake pan and sprinkle the remaining 1/2 cup of cheese on top.
Bake the cornbread for 35 minutes, until the top is light golden and a toothpick inserted in the center comes out clean. Transfer the cornbread to a rack to cool for 20 minutes. Run a knife around the edge of the cornbread, turn it out onto the rack and let cool slightly. Cut the cornbread into wedges and serve warm.