Grill the chiles and bell peppers until charred all over, 3 to 4 minutes per side, then immediately them to a large bowl and cover with plastic wrap to steam for 10 minutes. When cool enough to handle, peel and discard the blackened skins and remove the stems and seeds. Finely dice the peppers and set aside.
Preheat the oven to 375 degrees F.
Pour 4 1/2 cups water and 1 teaspoon salt in a heavy-bottomed pot set over medium-high heat and bring to a boil. In a slow, steady stream, add the cornmeal while whisking vigorously to incorporate and smooth out lumps. Reduce the heat to medium-low, and simmer, stirring continuously for the first 2 to 3 minutes. Cook the polenta until thick, and it begins to pull away from the sides of the pot, 35 to 40 minutes. Remove from the heat and stir in the diced peppers, the Pecorino-Romano and butter.
Grease a quarter-sheet tray with the oil. Pour the polenta on the prepared sheet tray and smooth out the top with a rubber spatula. Bake until golden brown and bubbling, 20 to 30 minutes. Cool to room temperature, then refrigerate for 1 hour.
Cut the polenta into squares, then brush the squares with olive oil and season with salt and pepper. Grill the polenta on both sides to create grill marks and heat through, 3 to 5 minutes. Keep warm until ready to serve.