Bring a medium pot of water to a boil and cook tomatillos 6 minutes. Add garlic and cook with tomatillos for 2 minutes more. Drain and rinse with cool water.
Add tomatillos, garlic, chiles, lime, oil, salt, cumin, and cayenne to a blender or the bowl of a food processor and process until combined but slightly chunky. Add cilantro and onion and lightly pulse to combine. Texture should remain slightly chunky. Season with salt if necessary.
Salsa can be made 5 days ahead. Chill in a resealable container.
