Grilled Filets Mignons

1A. FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour two-thirds evenly over grill, then pour remaining coals over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
1B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.
2. Meanwhile, pat steaks dry with paper towels and lightly rub with oil. Season steaks with salt and pepper.
3. Clean and oil cooking grate. Place steaks on grill (hotter side if using charcoal) and cook (covered if using gas) until well browned on both sides, 4 to 6 minutes, flipping halfway through cooking. Move steaks to cooler side of grill (if using charcoal) or turn all burners to medium (if using gas) and continue to cook (covered if using gas), until meat registers 115 to 120 degrees (for rare) or 120 to 125 degrees (for medium-rare), 5 to 9 minutes longer.
4. Transfer steaks to serving platter, tent loosely with aluminum foil, and let rest for 10 minutes before serving.