Preheat the oven to 400°F. Butter a 10-inch cast iron skillet or similar oven-safe baking dish.
On the stovetop in a medium-sized saucepan, whisk together the milk, salt, and cornmeal. Cook over medium heat, stirring constantly for about 3-5 minutes, until the mixture thickens to a pudding-like consistency. Remove from heat and let cool for 5 minutes
Stir the chive and onion cream cheese into the remaining cornmeal mixture in the saucepan.
In a medium bowl, beat the eggs. Add 2-3 Tbsp of the warm cornmeal mixture to the eggs to temper. Stir to combine.
Whisk the tempered eggs into the cornmeal mixture. Mix until fully combined.
To the mixture add the fresh chives and 1 1/2 cups shredded cheddar cheese. Spoon the batter into the skillet or baking dish. Sprinkle the top with the remaining 1/2 cup shredded cheddar cheese. Dot with butter.
Place in to the oven and bake for 25 to 30 minutes or until the center is set when gently shaken.