Preheat the oven to 400 degrees F and lightly brush a baking sheet with vegetable oil. Mix 2 tablespoons sour cream, the panko and egg in a large bowl; let sit 5 minutes.
Grate 1 carrot and 1 celery stalk into the bowl with the panko mixture. Add the meat, celery leaves, half of the scallions, the parsley, garlic, cayenne and 1/2 teaspoon salt and mix with your hands until combined. Dampen your hands and shape the mixture into 36 mini meatballs (about 1 inch each); arrange on the prepared baking sheet. Bake until browned and cooked through, about 12 minutes.
Meanwhile, melt the butter in a Dutch oven or large pot over medium-high heat. Add the remaining scallions and cook until wilted, 1 minute. Add the chicken broth, hot sauce and ketchup; bring to a boil, then reduce the heat to medium low. Simmer until the sauce thickens slightly, about 8 minutes. Add the meatballs; simmer until tender, about 8 more minutes.
Mix the blue cheese and the remaining 3/4 cup plus 2 tablespoons sour cream in a medium bowl. Cut the remaining 2 carrots and 2 celery stalks into sticks. Transfer the meatballs to a bowl and serve with the vegetable sticks and blue cheese dip.