Heat the Instant Pot using the saute function.
Add the ground beef and cook, stirring occasionally until the meat is browned and broken into small pieces, about 5 minutes.
Using a slotted spoon, remove the ground beef to a bowl but leave the drippings in the Instant Pot.
Add the onion and cook, stirring occasionally, until it is soft and just starting to brown, about 3 minutes.
Add the bell peppers, garlic, Italian seasoning, crushed red pepper flakes, and cook for an additional minute.
Next, add the diced tomatoes, beef stock, rice, and bay leaf. Add the ground beef back to the pot and stir to combine.
Attach the lid and ensure the valve is in the “sealing position” and set the Instant Pot to Pressure Cook - Manual for 4 minutes.
Once the Instant Pot has finished, allow the pressure to naturally release for 10 minutes.
Remove the lid and stir the soup.
Season with salt and pepper to taste and remove the bay leaf.
Serve the soup with your desired toppings and store any leftovers in an airtight container in the fridge for up to three days.