Prepare the marinade by whisking together all the ingredients in a non-reactive bowl.
Peel the shrimp and remove the tails. Partially butterfly each shrimp as you devein it, cutting a deep slit in the back. Stir the shrimp into the marinade so that all are submerged, cover tightly, and refrigerate for 1 hour.
Prepare the avocado tomatillo sauce by combining all of the ingredients in a blender or food processor. Process until smooth. Reserve.
Prepare the grill for direct grilling at 600°F, preferably over a charcoal fire.
Remove the shrimp and discard the marinade. Season the shrimp with salt and pepper. Grill over the hottest part of the fire, turning once, until the deepest part of the slit on the back of each shrimp turns opaque (about 5 minutes total). Quickly grill each tortilla on one side.
Assemble each taco by stacking a pair of tortillas (two tortillas are used for each taco). Spread a spoonful of sauce in the bottom. Add two shrimp, then top with cheese and cilantro leaves.