Preheat the oven to 400°F. Place a small cast iron skillet in the oven with the butter and allow it to melt while the oven heats.
In a medium bowl, whisk together the cornmeal, baking soda, and salt. Set aside.
In a separate bowl, whisk the buttermilk and eggs until well combined. Add the dry ingredients and stir just until the batter comes together—do not overmix.
Gently fold in the shredded cheddar cheese and sliced jalapeños until evenly distributed.
Carefully remove the hot skillet from the oven and swirl the melted butter to coat the bottom and sides. Pour the batter into the hot skillet, spreading it evenly.
Bake for 18–22 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Remove from the oven and let cool slightly before slicing and serving.