In a large bowl, whisk together flour, cornmeal, baking powder, baking soda and salt.
Make a well in the centre, then add buttermilk and eggs. Mix together until combined, then add slightly cooled melted butter. Mix until just combined, being careful not to overmix.
In a 9" cast iron skillet, melt other 2 tablespoons of butter on the stove over medium heat.
Pour batter into hot skillet. (The batter should sizzle.) Smooth out top as necessary. Dot the surface with dollops of tomato jam and lightly swirl into batter with a knife.
Cook batter on stovetop for 1 minute, then transfer to oven. Bake for 20–25 minutes until edges are crispy and a wooden pick inserted in the centre comes out clean with only a few fluffy crumbs attached.
Move skillet to a wire rack and allow cornbread to cool for 10 minutes before slicing and serving.
If you don't have buttermilk, mix 1 cup + 6 Tbsp (325ml) whole milk with 2 Tbsp white vinegar and let sit for 15 minutes.