Pat beef dry with paper towels and sprinkle with 1½ teaspoons salt and pepper.
Using highest sauté function, heat 2 tablespoons oil in Instant Pot until just smoking.
Add half of beef and brown on all sides, 6 to 8 minutes; transfer browned and unbrowned beef to bowl.
Add remaining 2 tablespoons oil to fat left in pot.
Add onion, carrot, and remaining 1½ teaspoons salt and cook, stirring occasionally, until vegetables are softened and lightly browned, 4 to 6 minutes.
Stir in tomato paste, garlic, anchovies, oregano, and pepper flakes and cook, stirring often, until mixture is fragrant and deeply browned, 1 to 2 minutes.
Stir in wine, scraping up any browned bits, and cook until nearly evaporated, about 1 minute.
Stir in tomatoes and Parmesan rind, if using.
Nestle beef into pot, along with any accumulated juices.
Lock lid into place and close pressure-release valve.
Select high pressure-cook function and cook for 45 minutes.
Turn off Instant Pot and quick-release pressure.
Carefully remove lid, allowing steam to escape away from you.
Discard Parmesan rind, if using.
Using potato masher, mash beef in pot until broken into bite-size pieces.
Season with salt and pepper to taste.
Stir in parsley.
Serve. (Ragu can be refrigerated for up to 3 days.)
