Preheat the broiler to high and line a baking sheet with foil.
Slice the pepper into four or five flat pieces around the stem, removing the veins and seeds.
Place the pepper pieces on the baking sheet, skin side up, and drizzle with 1-2 teaspoons of olive oil.
Broil the peppers for 3-4 minutes until they start to blacken in spots. Flip them and broil for an additional 2-3 minutes until they are soft and slightly charred.
Allow the peppers to cool slightly. For a smoother soup, remove the skins.
Chop the garlic, onion and parsley.
Dice the tomatoes and cucumber.
Place all the ingredients, including the roasted peppers, in a blender and blend on medium-low speed until smooth.
Cover the soup and let it sit in the fridge for 1 hour. Serve chilled, garnished with chopped fresh parsley, a drizzle of olive oil, and a sprinkle of paprika or ground black pepper.