Place poblanos directly over a gas flame or under a broiler set to high, turning occasionally, until blackened all over, about 8-10 minutes. Transfer to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes. Peel off most of the charred skin (some remaining is fine), then cut a slit down one side and carefully remove the seeds and membranes while keeping the pepper intact.

Heat olive oil in a large skillet over medium heat. Add onion and cook until softened and just starting to brown at the edges, about 5 minutes. Stir in garlic, cumin, smoked paprika, and oregano; cook until fragrant, about 30 seconds.

Add chopped shrimp to the skillet and cook, stirring frequently, until just pink and opaque, about 3-4 minutes. Remove from heat immediately to prevent overcooking. Stir in lime juice, half the cotija cheese, and cilantro. Taste and season with salt if needed.

Preheat oven to 400°F. Line a baking sheet with foil. Divide the shrimp filling among the four poblanos, packing it in gently but not overstuffed. Arrange on the baking sheet, slit side up. Top with shredded Monterey Jack and remaining cotija.

Bake until the cheese is melted and starting to brown in spots, about 12-15 minutes. Switch to broil for the last 2 minutes if you want more color on top. Let rest 5 minutes before serving. Garnish with extra cilantro and serve with lime wedges if desired.