1. Choose the right cut: Start by choosing a high-quality filet mignon cut, which should have a nice marbling of fat throughout, as this will result in a more tender and flavorful grilled steak.

2. Bring to room temperature: Allow your filet mignon to come up to room temperature for about 30 minutes before grilling. This ensures even cooking and better flavor.

3. Preheat the grill: Preheat your gas or charcoal grill to high heat (about 450°F / 230°C).

4. Prepare the grill grates: Clean your grill grates with a brush to remove any residue. Then, using tongs and a paper towel soaked in vegetable oil, grease the grates to prevent sticking.

5. Season the steak: Lightly coat both sides of the filet mignon with olive oil, then season with salt and freshly ground black pepper to taste.

6. Sear the steak: Place the filet mignon onto the hot grill grates and let it sear for 2-3 minutes on each side to create a nice crust.

7. Lower the heat: After searing, reduce the heat on your gas grill or move the steak to an area of lower heat on your charcoal grill.

8. Grill over indirect heat: Move your filet mignon over to indirect heat and close the grill lid for even cooking.

9. Time your cook: Continue cooking for 4-5 minutes per side for medium-rare (130°F / 54°C), 5-7 minutes per side for medium (135°F / 57°C), or 7-9 minutes per side for medium-well (145°F / 63°C).

10. Check internal temperature: Use a meat thermometer to check the internal temperature of your filet mignon at its thickest part for accurate cooking.

11. Let it rest: Remove the steak from the grill and let it rest on a cutting board, tented with aluminum foil, for about 5 minutes. This allows the juices to redistribute for a more tender and juicy steak.

12. Slice the filet mignon: After resting, cut your filet mignon against the grain into ½-inch slices for optimal tenderness.

13. Serve with your favorite sides: Plate your sliced filet mignon accompanied by your favorite side dishes, such as roasted potatoes, grilled asparagus, or a fresh garden salad.

14. Enjoy! You’ve now mastered the art of grilling the perfect filet mignon. Savor your delicious creation and impress your guests with your grilling skills, being sure to try out new seasoning and sauce combinations for an even more delectable experience.