Place the beans in a large bowl and cover with plenty of cold water. Soak for 8 hours or overnight, then rinse and drain the beans. Alternatively, use the quick soak method described here.
Sect the Sauté setting on the Instant Pot and let the pot heat up for a few minutes before adding the oil. Once the oil is hot, add the onion and bell pepper along with a pinch of salt and cook until the onions are translucent, 3-5 minutes.
Add the garlic and cook for 1 minute, tossing frequently to prevent burning.
Add the spices, salt, and pepper, and stir frequently until very fragrant and the vegetables are well coated with the spices, about 30 seconds.
Pour in the water to deglaze the pan, using a wooden spoon or spatula to scrape up any browned bits on the bottom of the pot. Add the soaked and drained beans, along with the brown rice, and stir well.
Pour the crushed tomatoes and tomato sauce on top and gently stir (don’t stir the tomatoes down too much, or they might sink to the bottom and block the Instant Pot’s heat sensor, causing it to burn).
Secure the lid and set the Pressure Release to Sealing. Select the Pressure Cook setting at high pressure and set the cook time to 12 minutes.
Once the 12-minute timer has completed and beeps, allow a natural pressure release for 15 minutes and then carefully switch the Pressure Release knob from Sealing to Venting to release any remaining steam.
Stir in the lime juice. Season to taste with additional salt and pepper as needed and garnish with the cilantro.