Preheat the oven to 400 degrees F. Line a baking sheet with foil.
Add the tomatoes, poblano, onions and garlic cloves to the prepared baking sheet. Toss with the oil to coat, and sprinkle with salt. Roast for 15 minutes. Remove the garlic, flip the poblano over, and continue roasting until the poblano and onions are charred and the tomatoes are soft and beginning to split, another 15 minutes. Let cool for at least 20 minutes.
Peel the garlic and remove the skin and stem from the poblano (remove the seeds, too, for a milder sauce).
Adjust the oven temperature to 350 degrees F.
In a food processor, combine the roasted vegetables, cilantro, vinegar, adobo sauce, coriander, cumin and 1/2 teaspoon salt. Process until evenly combined but still with some texture, similar to crushed canned tomatoes. Pour into a large saucepot and stir in the tomato puree and chicken stock. Bring to a boil and cook for 2 to 3 minutes, just to combine the flavors. Remove from the heat and season with salt.
Place the shredded chicken in a bowl, mix with 2 cups of the enchilada sauce and let marinate for at least 20 minutes. Taste and season with salt as needed.
Meanwhile, wrap the tortillas in foil and place in the oven for 10 to 15 minutes, until softened.
Spread 2 cups of the enchilada sauce on the bottom of a 9-by-13-inch broiler-proof baking dish. Remove the tortillas from the oven. To the center of each tortilla, add 1/4 cup of the marinated chicken, a sprinkle of Monterey Jack, and some enchilada sauce. Wrap the tortillas around the filling (they should be about the size of a cigar) and place seam-side down in the baking dish.
Pour the remaining sauce evenly over the enchiladas. Sprinkle with the remaining Monterey Jack and the olives. Bake on the center rack for 20 minutes, until the sauce just begins to bubble up around the edges. Turn the oven to broil and cook until the cheese has browned in spots, 2 to 3 minutes more. Remove from the oven and let cool for 15 minutes.
Serve the enchiladas with queso fresco, sour cream, avocado, cilantro and lime wedges.