Preheat your oven to 425°F (220°C). Pierce the eggplant and red bell pepper several times with a fork to allow steam to escape. Slice the top quarter-inch off the head of garlic to expose the cloves, then place it on a small piece of aluminum foil. Drizzle the exposed garlic with ½ tablespoon of the extra virgin olive oil and wrap it loosely in the foil.
Place the pierced eggplant, bell pepper, and foil-wrapped garlic directly on the baking sheet. Roast for 40-45 minutes, or until the eggplant is completely collapsed and wrinkled, the pepper's skin is blistered, and the garlic is soft and fragrant.
Carefully transfer the hot eggplant and bell pepper to a bowl and cover it tightly with a plate or plastic wrap. Let them steam for 10-15 minutes. This crucial step loosens the skins, making them effortless to peel. Allow the garlic to cool on the side.
Once cooled enough to handle, peel the skins from the eggplant and bell pepper; discard the skins, stems, and seeds. Squeeze the soft, caramelized garlic cloves out of their skins. Place the roasted eggplant flesh, bell pepper flesh, and roasted garlic into the bowl of a food processor.
Add the tahini, lemon juice, smoked paprika, cumin, and sea salt to the food processor. Process on low, slowly drizzling in the remaining 2.5 tablespoons of extra virgin olive oil until the mixture is smooth and creamy.
Stir in most of the chopped fresh parsley, reserving a sprinkle for garnish. Taste and adjust seasoning if necessary—it may need another squeeze of lemon or pinch of salt depending on your preference. Transfer the baba ganoush to a serving bowl, create a swirl with the back of a spoon, and garnish with a final drizzle of extra virgin olive oil and the remaining parsley.