Slide the garlic cloves onto a skewer, spacing them slightly apart. Brush the skewered garlic with 1 teaspoon of oil.
Place the whole bell peppers and skewered garlic directly on the grill rack over the heating elements of a gas grill. Cover the grill. Cook the garlic until the cloves are lightly browned, about 2 ½ minutes per side. Cook the peppers, rotating them as necessary, until the skin chars and blisters evenly, about 15 to 20 minutes.
While the peppers are hot, place them in a large bowl and cover the bowl tightly with plastic wrap. Allow them to steam for 5 minutes. Remove the peppers from the bowl and, peel the skin. The skin should slip off easily using your fingers. Remove the stem, the membranes, and the seeds from the peppers, and coarsely chop them, placing them in the bowl of a food processor.
Add the garlic, the remaining 2 tablespoons oil, paprika, smoked paprika, oregano, salt and pepper to the food processor along with the chopped red pepper. Pulse briefly until all ingredients are combined and starting to get chopped. Add the torn bread, and process, stopping to scrape down the sides of the bowl with a spatula, until the mixture is thick and smooth. Transfer to a bowl and let stand at room temperature for 1 hour to allow flavors to get to know each other. Taste, and adjust the seasonings with salt and pepper as desired.
Serve the dip with fresh veggies, crackers, or sourdough bread that’s been lightly brushed with olive oil and grilled until golden brown.