Turn on two gas-fired stovetop burners (or fire up the grill) and roast the peppers directly on the flames, turning them often with tongs, until fully blackened. Transfer the peppers to a bowl, cover tightly with plastic wrap, and let steam until cool enough to touch.
Rub off the black skins, cut out the stems, remove the seeds, and rip the peppers in half. Cut the pepper flesh into strips and then on the diagonal into 1-inch-wide diamonds.
Heat 2 tablespoons of the olive oil in a large skillet over medium heat. Add the garlic and cook, stirring, until it turns light golden brown. Add the peppers, season with ¼ teaspoon salt, a few cranks of pepper, and a pinch of sugar, and cook over medium-low heat, stirring occasionally, until the peppers soften and sweeten, about 15 minutes.
Meanwhile, for the sour orange vinaigrette, whisk together the remaining 1 tablespoon olive oil, ½ teaspoon salt, black pepper to taste, the red pepper flakes, and the orange and lemon juices.
Lay the cooked peppers out on a platter, drizzle with the sour orange vinaigrette, and top with the crumbled cheese. Serve warm or at room temperature, with grilled bread.