Press the Saute button on the Instant Pot. Wait until the front of the Instant Pot says "Hot," then add oil. When oil is hot, add the chicken breast cubes and chopped onion. Cook until the chicken is mostly white instead of pink and the onion is softened, about 3 - 4 minutes.
Then add a tablespoon of minced garlic and cook for about a minute.
Add the chicken broth and Worcestershire sauce. Deglaze the pan by scraping the bottom of the pot with a spatula to remove any food particles to prevent them from scorching.
Add the uncooked white rice, and salt, pepper, and ranch seasoning mix. Do not stir.
Press cancel to stop the sauté function. Secure the lid. Move the pressure valve to the sealing position. Press the pressure cook button or manual cook button, select high pressure, and adjust the time to pressure cook for 5 minutes. (It will take about 8 - 10 minutes for the Instant Pot to come up to pressure before the pressure cooking starts.)
While the Chicken and Rice are cooking, in a small bowl, stir together the milk and flour to make a slurry. Set aside until after the chicken and rice have finished pressure cooking.
While the chicken and rice are cooking, run hot water over the frozen broccoli to thaw. Drain the broccoli.
After the Instant Pot has finished the pressure cooking cycle, let it release pressure naturally for 10 minutes and then, using a long-handled spoon move the pressure valve to the venting position, to do a quick release of pressure. Wait for the pin to drop. Then carefully, remove the lid.
Immediately pour the milk and flour slurry into the chicken and rice mixture and stir.
Add the thawed broccoli to the chicken and rice.
Add the shredded cheese to the Broccoli Cheese Chicken And Rice Casserole.
Stir everything together until it is well combined and the broccoli and cheese have been evenly distributed throughout the chicken and rice mixture.