Place steak and pesto in a resealable plastic bag and marinate in the fridge at least 4 hours or overnight. Heat BBQ or stovetop grill to high. While the grill is heating, scrape the pesto from the steak to avoid scorching, and season the meat with salt and pepper. Grill the steaks, turning over once and moving to avoid flare-ups, about 6 to 8 minutes for medium-rare. Remove the steaks from the grill and allow them to rest before slicing them into thin diagonal strips.

Place the cream in a saucepot and bring the cream to a simmer over medium heat. Simmer until the cream is reduced by one third. Over low heat, slowly add the cheese and whisk until the cheese is melted and the mixture is smooth. Add the pepper and parsley and serve immediately or pour into a fondue pot set over low heat.