Press the Saute button and select High. Wait until the display says "Hot" and then add the oil. When the oil is hot add the chopped onions and cook for 3 minutes or so.
Add the minced garlic and cook for about 1 minute.
Add the carrots, celery, and ham.
Pour in 4 cups of chicken broth and 4 cups of water.
Add in the rinsed and drained dried beans.
Add in the Cajun Seasoning, Italian Seasoning, and salt (if desired) and pepper.
Place the lid on top of the Instant Pot and move the pressure release valve to the SEALING position. Pressure cook 45 minutes on High Pressure by pressing the MANUAL or PRESSURE COOK button. Adjust the timer to 45 minutes. Make sure it says High Pressure. (NOTE: It will take 10 to 20 minutes to come up to pressure before it starts the 45-minutes of pressure cooking.)
Do a natural release, which means that you do NOTHING and let the Instant Pot release pressure naturally until the pin drops.
After the Instant Pot has fully released the pressure, and the pin has dropped, open the lid and pour in can of diced tomatoes with the juice. Press Sauté to heat for 5 minutes. Garnish with chopped cilantro or parsley and serve.
Notes
Cajun Seasoning. You can use the Cajun Seasoning from the package of 15-bean soup or make my Homemade Cajun Seasoning or use a store-bought seasoning.
Salt. Depending on the brands of chicken broth and Cajun Seasoning you use, you may not need additional salt as many brands of chicken broth and Cajun Seasoning contain a significant amount of salt.