In the bottom of the Instant Pot, add the dry beans, water, whole chipotle pepper, cumin and oregano.
In an oven-safe bowl that is roughly 7-inches in diameter, add the brown rice, 1/4 teaspoon of salt, and 1 1/4 cups of water. Place a 2.5-inch trivet into the beans at the bottom of the pot, so you can place the bowl of rice on top of that.
Secure the lid to your Instant Pot and move the steam release valve to SEALING. Press the MANUAL or PRESSURE COOK button on your machine, then cook at high pressure for 30 minutes. It will take about 10 to 15 minutes for the Instant Pot to come to pressure before the cook cycle begins.
Once the cook cycle is complete, let the pressure naturally release for 10 minutes. The Instant Pot screen will read LO:10 when 10 minutes has passed. Move the steam release valve to VENTING to release any remaining steam pressure. When the floating valve in the lid drops, it's safe to open the lid.
Use oven mitts to remove the bowl of cooked brown rice, and the trivet from the beans. Use a spoon to remove the whole chipotle pepper (so you don't bite into that later), then stir the beans and test them to make sure they are tender by pressing one against the side of the pot with a fork. When they mash easily, you may season them with 1/2 teaspoon of salt. (If they are not tender, you can always return the lid and cook for 5 more minutes, but don't add salt until they are done.)
The beans will be sitting in a little bit of liquid, so you can use the SAUTE function if you'd like to get rid of that quickly. I've found that they become less watery the longer they sit in the pot, so I don't always use the saute function and simply serve them using a slotted spoon instead.
Serve the cooked rice and black beans with your favorite burrito bowl toppings, like shredded lettuce, salsa, guacamole, a squeeze of lime juice, and some fresh cilantro. I like to store the leftovers separately to keep them more visually appealing, but you can store them together for an easy-to-grab lunch later. Leftovers should keep in the fridge for up to a week.