Heat the olive oil in a large skillet over medium-high heat for 1 minute. Add the chopped chilies and 1/2 of the garlic and cook until the peppers start to soften, about 5 minutes. Add the tomatillos and 1 1/2 teaspoons of salt, reduce the heat to medium-low and cook until the tomatillos begin to break down and release some liquid, about 10 minutes, stirring occasionally.
Transfer the tomatillo sauce to your blender, puree, and set aside.
Melt the butter in a large skillet over medium-high heat. Add the shrimp, season them with some salt and pepper and the remaining chopped garlic. Cook until the garlic becomes fragrant, 1 to 2 minutes, stirring often. Add the tomatillo sauce and simmer until the shrimp are curled and opaque, 1 to 2 minutes. Serve sprinkled with the cilantro.