Mix ¼ cup oil, garlic, and lemon zest in a medium bowl. Let marinate for 20 minutes.
Add all herbs to oil mixture; stir until well coated. Let stand until herbs begin to wilt, about 10 minutes.
Stir in remaining ¼ cup oil, then red wine vinegar. Season salsa verde with salt and pepper.
Heat grill to high heat. Season skirt steak with salt and pepper to taste and grill until charred, 2 minutes per side for medium-rare.
Transfer steak to a serving platter; let rest for 5 minutes allowing juices to accumulate on the platter. Transfer skirt steak to a cutting board; slice against the grain on a diagonal.
Return the steak to the platter with its juices. Spoon half of herb salsa verde over steaks. Pass remaining herb salsa verde alongside when serving.