Soak the chickpeas in three times the amount of water overnight. Or inta-soak them in 6 cups of water. Close the sealing valve and cook for 5 minutes on High Pressure. Let the steam naturally release for 10 minutes. See notes for the quick-soak method.
Preheat the oven to 425F. (200 C.). Place the cleaned and quartered red peppers with the skins up on a parchment-lined baking tray. Roast the peppers for 20-25 minutes until the skins begin to brown.
If using dehydrated sundried tomatoes, soak them in a small bowl of hot water for a few minutes until they are soft enough to dice.
When the peppers are done, remove them from the oven and allow them to cool until you can handle them. Dice the peppers and set them aside.
Set the Instant Pot to Sauté and allow it to heat. After it beeps, add the red onions. Stir the onions frequently and cook them for about 3 minutes. Then stir in the garlic, smoked paprika, chili flakes, red peppers, sundried tomatoes, sherry vinegar, and diced tomatoes.
Turn the Instant Pot off. Add the broth or water, vinegar, and chickpeas. Use a wooden spoon to stir the ingredients and clean the bottom of the Instant Pot.
Place the lid on the Instant Pot and set the steam handle to Sealing. Set the Instant Pot on High Pressure for 20 minutes. Once the Instant Pot has stopped cooking, allow the steam to naturally release for 10 minutes. Carefully remove the lid and stir the soup.
While the soup cooks, gather the almonds, parsley, and red chili flakes on a cutting board. Bunch the ingredients together and carefully chop them.
Once the soup is done, stir and taste it. Add salt and pepper and adjust the other spices if desired.