Preheat the oven to 300 degrees F.
Roast the peppers by placing them on an open gas flame, turning them frequently with tongs until all the sides are charred black, 7 to 10 minutes. (Alternately, the peppers can be roasted under a broiler, or on top of a gas or charcoal grill.) Put the peppers in a plastic or paper bag, and cool for about 15 minutes.
Peel the peppers, remove the seeds and stems, and discard. Coarsely chop the peppers.
In a bowl, season the shrimp with the Essence, tossing to coat evenly. Heat 1 tablespoon of the oil in a large, non-stick skillet over medium-high. Add the garlic and cook, stirring, for 15 seconds. Add the shrimp and cook until the shrimp are just pink, 1 1/2 to 2 minutes. Remove from the heat and transfer to a plate to cool. Wipe the skillet clean.
In a bowl combine the 2 cheeses.
On a work surface, spread 3 of the tortillas. Sprinkle about 1/2 cup of the cheese over the bottom of each tortilla. Top each with 1/3 of the shrimp, mushrooms, and chiles. Sprinkle with 1/2 cup of the remaining cheese and top with a tortilla, pressing to adhere.
Add 1 teaspoon of the remaining oil to the pan over high heat. Add 1 assembled quesadilla and cook until the cheese starts to melt and the bottom starts to brown, about 3 minutes. Turn with a large spatula and cook until the bottom is golden brown, 2 to 3 minutes. Remove to a baking sheet and place in the oven to keep warm. Repeat with the remaining oil and quesadillas.
To serve, cut each quesadilla into 6 wedges and divide among plates. Serve with the poblano salsa on the side for dipping.
Yield: 4 servings