Press the "sauté" button on your Instant Pot then add the oil.
Give the oil a minute to heat up, then add the onion, bell peppers and carrots.
Sweat the vegetables for about 5 minutes, until they begin to soften up.
Add the garlic, chili powder, cumin, paprika, and cayenne pepper. Continue cooking until the mixture becomes very fragrant, about 1 minute. Hit the "cancel" button.
Stir in the water. Add the tomatoes, then and add the beans on top of the tomatoes. Do not stir.
Place the lid on your Instant Pot and set the valve to the "sealing" position. Press the "pressure cook" or "manual" button and set the pressure to high. Set the chili to cook for 10 minutes.
When the chili has finished cooking, carefully move the valve to the "venting" position. Let the pressure release completely.
Remove the lid from the Instant Pot and stir in the corn and tomato paste, if using. Let the chili sit for a bit to thicken up, if desired.
Season the chili with salt and pepper to taste.
Ladle into bowls and serve.