Heat oil and garlic in a medium saute pan over medium-high heat. Cook, stirring occasionally, until garlic is pale gold, about 7 minutes. Remove from heat and add rosemary sprigs, turning them over several times, then set pan (with garlic and rosemary) aside.
Heat a large, seasoned cast-iron skillet or stove-top grill over high heat. When the pan is very hot, add the steaks, which should sizzle instantly and quickly begin to smoke. Cook until very brown on one side, 2-3 minutes; then turn steaks over, sprinkle with salt, and cook for another 3 minutes (the steaks should be very rare).
Remove skillet from heat and transfer steaks to a cutting board. Slice them on an angle, across the grain, into 1⁄2"-thick slices.
Return pan with garlic and rosemary to stove and heat over medium-high heat. When oil begins to heat up, add the steak slices together with any juices on the cutting board. Cook about 1 minute, turning frequently and seasoning generously with black pepper.