Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper. Cut the bell peppers into quarters and remove the stems, seeds, and membranes.
Arrange the peppers, onion, and garlic on the prepared baking sheet. Drizzle everything with olive oil and sprinkle with salt, black pepper, and smoked paprika.
Roast for 45 to 50 minutes, tossing the vegetables halfway through, until the peppers are very tender and beginning to develop browned edges.
Remove the roasted vegetables from the oven and let them cool for several minutes. If desired, peel away any loose skin from the peppers for an especially smooth dip.
Transfer the roasted peppers, onion, and garlic to a food processor. Add the red wine vinegar and any flavorful oil remaining on the baking sheet.
Blend for 1 to 2 minutes until the mixture is completely smooth and creamy. Taste and adjust the salt, pepper, or vinegar according to your preference.
Transfer the dip to a serving bowl, drizzle with a little olive oil, and garnish with fresh parsley. Serve warm, at room temperature, or chilled.