1 Sear the chicken: Season the chicken breasts all over with the salt and pepper.
Select the Sauté setting on your electric pressure cooker and heat the oil for 3 minutes, until shimmering. Using a pair of tongs, lower the chicken breasts into the pot and sear them for 3 minutes per side (6 minutes total), until lightly browned. Transfer the chicken to a dish.
2 Cook the onions and garlic: Add the onion to the pot and sauté for about 2 minutes, until it starts to soften. Add the garlic and sauté another 30 seconds or so, just until it is no longer raw.
3 Assemble everything in the pressure cooker: Add the water and use a wooden spoon to nudge any browned bits off of the bottom of the pot. Add the chicken back to the pot, nestling it in with the onions and garlic.
Lower a tall metal steam rack into the pressure cooker, making sure all of its legs are touching the bottom of the pot. Arrange the sweet potatoes on top of the rack in a single layer.
4 Pressure cook the potatoes and chicken: Secure the lid on your pressure cooker in its Sealing position. Cancel the Sauté program, then select the Manual or Pressure Cook program for 10 minutes at high pressure. (It will take about 10 minutes for the pot to come up to pressure before the cooking program begins.)
While the recipe cooks, line a sheet pan with foil and set it aside.
5 Release the pressure: As soon as the cooking program ends, perform a quick pressure release by moving the Pressure Release to its Venting position, releasing the steam. (At this point, the pressure cooker can be left on the “Warm” setting for up to 10 hours.)
Use tongs to gently transfer the sweet potatoes to the foil-lined sheet pan. Remove the chicken to a cutting board or dish.
6 Make the BBQ sauce: Stir the barbecue sauce in with the liquid and onions in the pot. Cancel the Keep Warm program, select the Sauté setting, and let the mixture boil and reduce for 8 to 10 minutes, stirring occasionally, until thick and glazy (the timing will vary slightly depending on how much sugar is in your barbecue sauce).
7 While the sauce is reducing, use a pair of forks to shred the chicken.
8 Mix the chicken with the BBQ sauce: Turn off the Sauté program. Add the chicken back to the pot and toss to combine.
9 Stuff the potatoes and broil: (You can skip this step if you like. Everything is already cooked through—it’s just to get the cheese bubbly and browned.)
Heat your broiler to high with a rack positioned a few inches below the heating element.
Split the sweet potatoes in half lengthwise, then stuff them with the chicken mixture. Top each sweet potato with two tablespoons of shredded cheese.
Broil for 2 to 3 minutes, until the cheese is bubbly and beginning to brown in spots. Remove from the oven, then sprinkle with cilantro and green onions. Serve hot.
Leftovers will keep for 3 to 4 days and can be reheated in the microwave.