Heat a cast iron pan over medium-high heat with some cooking oil in the bottom. Or, if you prefer to use the Instant Pot, add the oil there and press the sauté button.
You can cut the roast into four pieces if you want to increase the surface area of the beef for better browning.
Liberally salt both sides of the chuck roast. Once the pan is hot, place the beef in it. Cook until you achieve a nice brown sear on one side, then flip and repeat. Remove the beef to a plate and set it aside temporarily
Cooking the pot roast
Add the chopped garlic to the pan or pot. Cook until it just softens. Don't burn it! The garlic only needs about a minute.
Now pour in about ½ cup of the beef stock and scrape all the brown bits off the bottom of the pan. I like using a metal spatula for this.
Now it's time to add everything to the Instant Pot. If you used a pan to brown the roast, transfer everything from the pan into the Instant Pot.
Add the remaining beef stock, tomato paste, and chopped oregano. It's important to taste the cooking liquid—it needs to be really flavorful. Test it first, then add any salt and/or pepper as needed. If you think it needs more oregano, add that as well.
Set the Instant Pot to high pressure and cook for 1 hour and 30 minutes. You can either use the manual release or allow for a natural release at the end.
Prepare the orzo
Add the orzo to a pot along with 2 tablespoons of oil (or butter, if you prefer). Heat the pan over medium heat
Stir the orzo occasionally until it develops some brown color
Add 2 cups of water and bring it to a boil
Place a lid on the pot and remove the orzo from the heat.
Allow the orzo to sit undisturbed for 10 to 15 minutes, or until it's cooked through.
Final Prep
While the orzo is cooking, add the carrots to the Instant Pot. Press the sauté button and cook until the carrots are softened. Then, you can set the Instant Pot to 'Keep Warm' or turn it off.
Use a fork to break up the pot roast and serve it over the orzo with the carrots. Offer feta and additional oregano as optional toppings, if desired.