Add the olive oil to your 5 or 6 quart electric pressure cooker and turn on to saute function. When the pot is heated, add the diced onion. Saute for 3 minutes, or until translucent.
Add the chicken broth to the onions and using a wooden spoon scrape the browned bits off of the bottom so they don't burn during cooking. Turn the pressure cooker off of saute function.
Add the salsa verde, cumin and rice. Do NOT stir in the rice. Nestle the chicken breasts on top of the rice mixture. Sprinkle with salt.
Place the lid on the pressure cooker and cook on high pressure for 10 minutes with a 10 minute natural pressure release. (When the 10 minutes is completed cooking, let the pot sit for 10 more minutes until you release the pressure manually.)
Remove the chicken from the pot and fluff the rice. Place the chicken back on top of the rice and top with the shredded cheddar.
Place the lid back on the pressure cooker and let sit for 3-4 minutes, or until the cheese is melted from the heat of the pot.
*Optionally top with sour cream and cilantro.