Preheat your oven to 250°C (482°F).
Wash and scrub the potatoes thoroughly. Cut them into bite-sized chunks.
Rinse the peppers, remove the seeds, and slice them into strips.
Place the potatoes and peppers on a baking tray lined with parchment paper. Drizzle 2 tablespoons of olive oil over them and sprinkle with salt. Toss to coat evenly.
Take the heads of garlic and slice off the tops to expose the cloves. Drizzle a little olive oil over each head of garlic. Place them on the baking tray with the potatoes and peppers.
Bake in the preheated oven for 25 minutes. After 25 minutes, remove the garlic from the tray and set aside.
Continue baking the potatoes and peppers for an additional 10-15 minutes or until they are tender and slightly browned.
While the vegetables are baking, prepare the dressing. In a small bowl, whisk together 4 tablespoons of olive oil, lemon juice, honey, paprika powder, chili flakes, Italian herbs, pepper, and salt. Adjust seasoning to taste.
Once the vegetables are cooked, transfer them to a large mixing bowl. Squeeze the roasted garlic cloves out of their skins and add them to the bowl.
Pour the prepared dressing over the roasted vegetables.
Sprinkle shaved Parmigiano over the salad according to your taste preference.
Tear the basil leaves into small pieces. Add them to the bowl.
Gently toss everything together until well combined and evenly coated with the dressing.
Serve the roasted peppers potato salad warm or at room temperature as a delicious side dish or light meal.