Make cornbread: Preheat oven to 400°F. Whisk together flour, cornmeal, baking powder, salt, and baking soda in a bowl. Whisk together sour cream, milk, honey, eggs, and jalapeños in a second bowl.
Melt butter in a 10-inch cast-iron skillet over medium heat. Pour butter into sour cream mixture and whisk to combine. Add wet ingredients to dry and stir until blended. Transfer batter to skillet and smooth top.
Bake until golden brown and a toothpick inserted in center comes out clean, 20 to 25 minutes.
Make honey butter: Stir together butter, honey, and a pinch of salt in a bowl. Serve cornbread warm with honey butter.
