Place the poblano peppers directly on a gas flame or under a broiler, turning occasionally, until the skins are charred and blistered. Transfer them to a bowl and cover with plastic wrap or a lid to steam for 10 minutes. Once cooled, peel off the skins, remove the seeds, and roughly chop the peppers. Set aside.
Bring a large pot of salted water to a boil and cook the pasta according to the package instructions. Drain, reserving 1/2 cup of pasta water, and set aside.
Heat the olive oil in a large skillet over medium heat. Add the chopped onion and cook until softened about 3-4 minutes. Stir in the minced garlic and cook for 1 minute until fragrant.
Add the butter to the skillet, allowing it to melt. Sprinkle in the flour, stirring constantly for 1-2 minutes, to cook out the raw flour taste. Gradually whisk in the chicken or vegetable broth, ensuring a smooth mixture.
In a blender or food processor, combine the roasted poblano peppers, heavy cream, sour cream, cumin, sugar, and lime juice (if using). Blend until smooth and creamy.
Pour the poblano mixture into the skillet with the roux, stirring to combine. Simmer the sauce over low heat, allowing it to thicken slightly, about 3-5 minutes. Season with salt and black pepper to taste.
Add the cooked pasta to the skillet and toss to coat evenly in the sauce. If the sauce is too thick, use the reserved pasta water, a few tablespoons at a time, to reach your desired consistency.
Serve the creamy poblano pasta immediately, garnished with fresh cilantro if desired. Pair it with a light side salad or crusty bread for a complete meal.