To prepare the shrimp: Mix all the ingredients, except for the shrimp and olive oil, into a bowl. Add the shrimp; coat well with the rub and set aside
Preheat oven to 350 degrees F.
For the sauce: In a baking dish, toss together tomatillos, onion, jalapeno and garlic. Toss with extra-virgin olive oil and season, to taste, with salt and pepper. Roast until tender and caramelized, about 20 minutes. Remove from pan and cool for about 5 minutes then add to a food processor. Add avocado, lime juice and cilantro and blend until smooth. Season, to taste. Pour into a large bowl and chill.
Meanwhile, preheat grill to medium-high.
Remove the shrimp from the bowl and brush with oil. Place on the grill. Cook until the meat is opaque. Remove from heat to a platter and serve with the tomatillo salsa.
Garnish with lime zest, diced tomato, and chopped cilantro.