Preheat the oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Make the shawarma seasoning: combine ground cumin, turmeric, paprika, coriander, cinnamon, ground ginger, cardamom, and black pepper in a small bowl and mix well.
Toss the cauliflower florets with the oil and 1 tablespoon of the shawarma seasoning until evenly coated.
Spread the seasoned cauliflower in a single layer on the prepared baking sheet.
Roast for 25 to 30 minutes, turning once if desired, until the cauliflower is tender and lightly browned.
While the cauliflower roasts, make the sauce by stirring together the sour cream or Greek yogurt, minced garlic, and dill; season with salt and pepper to taste.
Serve the roasted cauliflower warm with the garlic-dill sauce on the side.