Preheat the Oven: Start by preheating your oven to 400°F (200°C).
Prepare the Brussels Sprouts: In a large bowl, toss the halved Brussels sprouts with olive oil, garlic powder, onion powder, salt, black pepper, and red pepper flakes if using. Ensure the sprouts are evenly coated.
Roast the Brussels Sprouts: Spread the seasoned Brussels sprouts in a single layer on a baking sheet. Roast in the preheated oven for 20-25 minutes, or until they are golden brown and crispy, flipping halfway through for even cooking.
Make the Cheesy Herb Dip: While the Brussels sprouts are roasting, prepare the dip. In a medium bowl, mix the softened cream cheese and sour cream until creamy and smooth. Stir in the shredded cheddar, parsley, chives, dill, lemon juice, salt, and pepper. Adjust seasoning to taste.
Serve: Once the Brussels sprouts are roasted, remove them from the oven and let them cool slightly. Serve warm on a platter alongside the cheesy herb dip for dipping.