Preheat the oven to 400°F.
In a small skillet over medium-high heat, sauté the finely diced jalapeños until they begin to brown slightly. There’s no need for oil—this step will be quick. Transfer the peppers to a bowl and allow them to cool.
In a separate small saucepan, melt 4 tablespoons of butter over low heat. Set aside to cool slightly.
Use the softened butter to thoroughly grease a 10-inch cast iron skillet or an 8x10-inch baking pan. Ensure an even coating to prevent sticking.
In a large mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, salt, and Tajín or cayenne pepper.
In a separate bowl, lightly beat the eggs. Add the buttermilk, runny honey, hot honey, and melted butter. (Tip: Spraying the measuring cup with non-stick spray before pouring the honey will help it release more easily.) Stir until well combined.
Make a well in the center of the dry ingredients and pour in the wet mixture. Gently fold the ingredients together, being careful not to overmix—it’s fine if a few streaks of flour remain.
Add the grated cheddar cheese, cubed cheese, and cooled jalapeños. Stir once more to evenly incorporate everything.
Pour the batter into the prepared skillet or baking pan, spreading it out evenly.
Bake in the center of the oven for 28–30 minutes. The cornbread should be fully set, and a skewer inserted into the middle should come out clean or with just a few crumbs.
Let the cornbread cool in the pan for about 30 minutes before slicing. Serve warm for the best texture and flavor.