Preheat oven to 425°. Place 3 tablespoons oil in a 13×9-inch baking pan. Place pan in oven until very hot, about 5 minutes.
In a large bowl, whisk together cornmeal, flour, baking powder, paprika, salt, and baking soda. In a small bowl, whisk together buttermilk, eggs, and remaining 3 tablespoons oil. Make a well in center of dry ingredients; add buttermilk mixture, stirring until combined. Spoon batter into hot pan, spreading evenly. Arrange peppers on top of batter.
Bake until a wooden pick inserted in center comes out clean, 15 to 17 minutes. Let cool in pan on a wire rack for 30 minutes before cutting into squares. Serve with Green Chile-Garlic Butter.
Recipe by Louisiana Cookin' at https://louisianacookin.com/smoked-paprika-buttermilk-cornbread/