Preheat the oven, then toss cubed potatoes and drained chickpeas with olive oil, thyme, rosemary, salt, and pepper. Add a halved lemon and garlic head (top sliced off). Roast for 45 minutes until golden, removing lemon and garlic after 30 minutes.
Blend roasted lemon juice, roasted garlic cloves, Greek yogurt, feta, roasted red pepper, black pepper, and a spoon of red pepper oil until smooth. Chill briefly to thicken. Avoid over-blending to prevent the dip from getting runny.
Dice the remaining roasted red pepper, walnuts, and parsley. Combine with a small drizzle of olive oil and optional lemon juice for a chunky, flavorful dressing.
Spread the feta dip on a serving plate. Toss roasted potatoes and chickpeas with most of the walnut dressing, then place on top of the dip. Sprinkle remaining dressing and optional chili flakes over the top for a beautiful presentation.