Preheat oven to 375°F. Grease a 9-inch cast iron skillet, or butter and flour a 9-inch round cake pan.
In a large bowl, sift together the flour, cornmeal, sugar, baking powder, baking soda, salt, and thyme. In a separate bowl whisk together the buttermilk, butter, vegetable oil, egg and egg yolk. Pour wet ingredients on top of the dry ingredients and gently stir together. Fold in the corn kernels. Do not overmix, batter should be somewhat lumpy.
Poor batter into the prepared pan and bake until top is golden, 30-35 minutes. Serve warm or at room temperature.
Store cornbread in an airtight container at room temperature for up to several days.
Calories: 303kcal, Carbohydrates: 41g, Protein: 6g, Fat: 13g, Saturated Fat: 8g, Cholesterol: 59mg, Sodium: 261mg, Potassium: 289mg, Fiber: 3g, Sugar: 11g, Vitamin A: 294IU, Vitamin C: 2mg, Calcium: 102mg, Iron: 2mg