Add the 4 tablespoons of softened butter, 1 teaspoon of honey, and a pinch of salt into a bowl. Mix until well combined and set aside. Preheat the oven to 375℉.
In a separate bowl whisk together the flour, cornmeal, baking powder, baking soda, and kosher salt until the ingredients are evenly combined.
In another large bowl add in the eggs, granulated sugar, 1 tablespoon of honey, 4 tablespoons of melted butter, vegetable oil, and buttermilk. Mix until well combined then pour in the bowl of dry ingredients. Gently mix until the batter is about 75% of the way combined. Add in the monterey jack cheese that's been tossed in flour, drained green chilies, and chopped chives. Fold in the ingredients until everything is evenly combined.
Spray a muffin tin with cooking spray. Add about a ½ teaspoon of the honey butter mixture into the bottom of each muffin cup. Then add a shallot round slice on top of the butter. Gently press down on the shallot slice so the butter on the bottom spreads. Add a scoop of the cornbread batter on top. The muffin cups should be about ¾ of the way full.
Bake the cornbread in the oven for about 16-18 minutes until a toothpick comes out clean. Allow it to rest in the pan for about 5 minutes before removing. Remove the cornbread muffins from the tin and invert them so the shallot side is up. If needed, run a knife around the edges and use an offset spatula to help lift the muffins out of the tin. Enjoy!