Combine flour, salt, and pepper in a mixing bowl; cover the roast with the mixture.
Warm oil in an Instant Pot on saute mode. Then, add the roast and brown the meat on all sides, 4-5 minutes per side to create a crust.
Add butter, onions, and pepperoncini's, then place the lid on the pot, but do not secure it. Let it simmer for 5 minutes.
Meanwhile, prepare the ranch dressing. Combine the ingredients for the ranch dressing in a small bowl and whisk to emulsify.
Remove the lid and add the ranch dressing.
Secure the lid, and set the Instant Pot to manual high pressure. Allow the meat to cook for 70 minutes with a quick release. When it's done, let it rest on a cutting board for about 5 minutes.
Shred the roast, and then add it to a serving dish with some liquid from inside the Instant Pot.
Serve the Mississippi roast as is, or throw it all on a hoagie with provolone cheese and a side of au jus.