Preheat the oven to 425°F* (220°C) and line a large baking sheet with parchment paper. Set aside.
To a medium mixing bowl, add the cream cheese, buffalo sauce, and whole milk (if using). Using a hand mixer, mix until the mixture is smooth and creamy, scraping down the sides of the bowl as needed.
Add the shredded chicken, sharp cheddar, and mozzarella cheese to the bowl. Stir until all the chicken is coated in the creamy cheese mixture and everything is evenly combined. This makes about 3 cups of the filling.
Spoon the buffalo chicken filling into each jalapeño half, mounding the mixture slightly but leaving a little space for the filling to expand as it melts.
Arrange the filled jalapeños on the prepared baking sheet, cut side up.
Bake for 16-18 minutes, or until the filling is hot, the cheese is melted, and the tops are lightly golden.
Let the poppers cool for about 5 minutes before serving. (The filling will be very hot inside.)
Garnish with drizzles of buffalo sauce and ranch dressing, or serve extra on the side for dipping.