Cook the soup: Add the tomato paste, cumin, paprika, salt and optional cayenne pepper and cook for one minute, while stirring constantly. Add the peeled red peppers and vegetable stock and stir. Bring the soup to a gentle boil, then reduce heat to maintain a simmer and cook for 15 minutes, stirring occasionally.
In a 3½ quart or larger Dutch oven or heavy-bottomed pot, warm 2 tablespoons of olive oil, then add the chopped onion, peeled whole garlic cloves and a sprinkle of salt. Sauté, stirring occasionally, until the onions are softened and turning translucent, about 5 to 8 minutes.
Steam and peel the peppers: Once the peppers are deeply blackened, remove them from the oven and use kitchen tongs to transfer the peppers to a medium-sized bowl and cover (or transfer them to a plastic bag and seal). Let the peppers steam for at least 10 minutes. Remove the cover and let them cool until they are manageable. Use your fingers to peel off the charred top layer of skin and discard (you may want to wear kitchen gloves for this). Peel the skin off the garlic, too.
Roast the peppers: Preheat oven to 450 degrees Fahrenheit with racks in the upper third and lower third of the oven. Arrange your halved peppers, cut side down, in a single layer on a large, rimmed baking sheet (use two sheets if necessary). Place the whole cloves of garlic in between the peppers. Roast on the upper rack (and lower rack, if you're using two baking sheets) until peppers are blackened across the top, around 20 minutes.