Whisk together oil, vinegar, garlic, salt, granulated sugar, and pepper in a medium bowl. Set aside ¼ cup vinaigrette in a small bowl. Whisk cheese, mayonnaise, sour cream, and chives into remaining vinaigrette (about ½ cup); set aside.
Place iceberg wedges on a large platter. Brush cut sides of wedges liberally with reserved ¼ cup vinaigrette. Set aside to marinate in dressing.
Cook bacon in a large nonstick skillet over medium-high, flipping occasionally, until rendered and almost crisp, about 8 minutes. Sprinkle one side of bacon slices with 1 tablespoon brown sugar; flip and cook 1 minute. Sprinkle with remaining 1 tablespoon brown sugar; flip and cook 1 minute more. Add vinegar, and let reduce until almost evaporated, about 30 seconds. Transfer bacon to a wire rack set inside a rimmed baking sheet; let stand 5 minutes.
Spoon Gorgonzola dressing over iceberg wedges on platter. Snap bacon slices in half; place one half over each iceberg wedge. Sprinkle wedges evenly with tomatoes. Nestle a slice of cheese on top of each wedge. Garnish with additional chives. Sprinkle with pepper to taste; serve immediately.
