Preheat oven to 400°F. Line a rimmed sheet pan with parchment paper and set aside.
Melt the butter in a heavy-bottomed small saucepan over medium heat. Add the finely diced onions, celery, and carrots. Sprinkle with the salt, and stir to evenly coat everything in the melted butter. Lower the heat and sweat the mixture for 4 to 5 minutes, or until the onions have become translucent at the edges and the carrots and celery have softened slightly. If the mixture dries out before you can reach that point, you can add 1 teaspoon of water at a time until the carrots and celery reach that stage.
Add the garlic to the pan and stir, cooking just until aromatic; about 1 to 2 minutes more.
Transfer the mixture to a large bowl. Let it rest for 5 minutes to cool.
Add the 1/2 of a cup of the Buffalo sauce, panko bread crumbs, and eggs and mix thoroughly. Add in the ground chicken, bleu cheese crumbles, and chopped parsley and mix gently until even.
Using a disher or cookie scoop for ease, divide the mixture into 30 meatballs, rolling each one gently to help shape it. Place them onto your prepared baking sheet with at least an inch of space surrounding each meatball.
Using another 1/4 cup of the Buffalo sauce, gently brush the tops of the meatballs.
Bake for 14 to 16 minutes, or until a thermometer inserted in the center of a meatball reads 165°F.
Transfer the meatballs to a large, heatproof mixing bowl. Pour the remaining 3/4 cup of Buffalo sauce over the meatballs and gently toss to coat.