Combine the onion, scallion whites, poblanos, 3/4 cup corn and the olive oil in a large pot over medium-high heat. Season with a big pinch each of salt and pepper and cook, stirring occasionally, until the vegetables are tender but not browned, 5 to 7 minutes. Add the tortillas and coriander and cook, stirring, until combined, about 1 minute. Add the chicken broth and tomatoes and bring to a boil. Season the chicken with salt and add to the pot. Reduce the heat to medium and simmer until the chicken is cooked through, 12 to 15 minutes. Remove the pot from the heat; remove the chicken to a plate.
Working in two batches, transfer the soup to a blender and carefully blend until very smooth (the liquid will be very hot). Clean out the pot and return the soup to the pot; season with salt.
Shred the chicken with your fingers. Thin the sour cream with 1 tablespoon water. Heat the remaining 1/2 cup corn in the microwave until just hot, about 30 seconds.
Divide the soup among bowls. Top with the sour cream, chicken, corn and scallion greens.