Line a baking sheet with parchment paper, then add the peppers.
Broil the peppers about 6 inches from the heat.
When the peppers are black on top, use long-handled tongs to turn them.
Continue this process until the peppers are blackened on all sides.
Put the red peppers in one bowl and the yellow peppers in a separate bowl, then cover both with kitchen towels or cloth napkins and allow them to sit for 10-15 minutes.
Peel and discard the skins, then remove and discard the seeds and stems. Return the peppers back to their bowls when finished, still keeping the red and yellow peppers separated.
Heat the olive oil in a skillet over medium-low heat. Once hot, add the onion and garlic, then sauté for 5 to 10 minutes or until the onion is tender. Remove from heat.
Combine the yellow peppers, half of the onion mixture, and 2 cups of vegetable stock in a blender. Process until the mixture is completely smooth, then pour into a 2-3 quart saucepan.
Wash out the blender, then add the red peppers, the remaining onion mixture, and the remaining 2 cups of vegetable stock. Process until the mixture is completely smooth, then pour into a separate 2-3 quart saucepan.
Bring both pepper mixtures to a boil, then cover and reduce the heat to low. Simmer for 10 minutes, then remove from heat.
Add the vinegar, salt, and pepper to taste to the red pepper mixture only.
Stir both soups, then pour about ½ a cup of each into separate measuring cups.
Simultaneously pour the two pepper soups into either side of a soup bowl.
Repeat until all of the soup has been poured into serving bowls.