Thaw shrimp if frozen. Peel and devein shrimp. Rinse shrimp; pat dry with paper towels. Cover and chill until needed.
Preheat broiler. Line a 15x10x1-inch baking pan with foil; lightly coat foil with cooking spray. Place whole tomatoes in prepared baking pan. Broil about 4 inches from the heat for 10 to 12 minutes or until skins are charred, carefully turning once halfway through broiling. When tomatoes are cool enough to handle, peel over a medium bowl to catch the juices. Remove tomato cores; discard cores and skins. Place tomatoes and juices in a food processor or blender. Cover and process or blend with several on/off pulses until nearly smooth; set aside.
Preheat oven to 425 degrees F. Line a large baking sheet with foil. Cut poblano peppers in half lengthwise; remove stems, seeds, and membranes. Place pepper halves, cut sides down, on prepared baking sheet. Roast for 20 to 25 minutes or until peppers are charred and very tender. Bring foil up around peppers and fold edges together to enclose. Let stand about 15 minutes or until cool enough to handle. Using a sharp knife, loosen edges of skins; gently pull off skins in strips and discard. Cut peppers into 1/2-inch-wide strips; set aside.
In a Dutch oven heat oil over medium heat. Add onion; cook for 8 to 10 minutes or until golden, stirring frequently. Add garlic, dried or snipped oregano, cumin, salt, pureed tomatoes, and roasted peppers. Bring to boiling over medium-high heat. Boil gently, uncovered, for 7 to 8 minutes or until mixture is quite thick, stirring frequently. Stir in broth. Return to boiling; reduce heat. Simmer, covered, for 30 minutes.
Stir in shrimp. Simmer, uncovered, for 2 to 3 minutes more or until shrimp are opaque.
Ladle soup into bowls. Top with cheese and, if desired, cilantro and oregano sprigs.