Warm the chicken broth in a small saucepan. Heat a large Dutch oven over medium heat. Add the butter and cook until melted, then add the onions, celery, poblanos, 1 teaspoon salt and 1/2 teaspoon pepper. Cook, stirring frequently, until the vegetables begin to soften and the onions are translucent, about 5 minutes. Add the garlic and cook for an additional 2 minutes.
Raise the heat to high, add the chicken broth and bring to a simmer. Add the mashed potatoes and use a wooden spoon or a whisk to incorporate them into the broth. The potatoes should melt into the broth, leaving no lumps. Bring the mixture to a boil, then turn the heat down to low, cover and simmer for 10 minutes.
Add the frozen corn and cook until the corn is heated through, about 2 minutes. Season to taste with salt and pepper. Ladle the soup into bowls and garnish with chives.
Feel free to use any type of leftover mashed potatoes you have on hand.