Start the Soup: Heat 1 tablespoon of olive oil in a medium pot over medium heat. Add the diced onion and poblano chile, cooking for 7 to 10 minutes until they soften. Stir in the garlic, cumin, and chipotle, and cook for another minute to release the flavors. Add the chicken stock, whole tomatoes (breaking them into smaller pieces with a spoon), shredded chicken, and kosher salt. Bring the mixture to a simmer and let it cook for 20 minutes, stirring occasionally.
Prepare the Tortilla Strips (Optional): If you're making homemade tortilla strips, slice the tortillas into ½-inch-wide strips, cutting any longer strips in half for easier handling. Heat the remaining ⅓ cup of olive oil in a medium skillet over medium-high heat. To check if the oil is hot enough, add one tortilla strip; it should sizzle. Fry the tortilla strips in small batches, flipping them as needed, until they are golden brown, about 1 to 2 minutes per batch. Remove the strips and place them on a paper towel-lined plate to drain excess oil. Sprinkle the strips with a little salt while they’re still warm.
Assemble and Serve: Pour the hot soup into bowls and top each serving with a handful of tortilla strips, if using. Add your choice of garnishes, such as a dollop of sour cream, diced avocado, sliced scallions, fresh cilantro leaves, and a lime wedge on the side. Serve immediately and enjoy.