Heat the oil in a large skillet over high heat.
Season both sides of steaks with salt and pepper then add to the skillet and cook for 4 to 5 minutes per side; remove from skillet and keep warm.
Reduce skillet heat to medium then add the broth and whisk up all of the browned bits from the bottom of the pan.
Add pineapple, brown sugar, vinegar and nutmeg to the skillet; cook for 5 to 7 minutes or until mixture is reduced into a thick, sweet and tangy pineapple topping. Add rum (or broth) and simmer for 2 minutes.
Serve pineapple sauce over steaks.