Preheat oven to 425°F. Add butter to a 10 inch cast iron skillet and place in the oven on the middle rack.
Allow the butter to melt, then heat until it begins to brown, about 15 minutes.
While the butter is heating, measure the flour, cornmeal, baking powder, baking soda, sugar, and salt in a large mixing bowl. Make a well in the centre.
Core and finely chop one small jalapeño. Slice the top of the second jalapeño into 6 - ¼ inch rounds. For added heat, finely dice the rest of the second jalapeño.
Crack eggs into a second mixing bowl then add sour cream and buttermilk and whisk together well.
Once the butter has browned, remove hot skillet from the oven and carefully pour most of the brown butter in a heat proof measuring cup. Leave about 1 tablespoon butter in the skillet.
Slowly pour and whisk the hot butter into the egg mixture. Pour the wet ingredients into the well in the dry ingredients and stir until just moistened.
Gently mix in the shredded cheddar cheese and finely diced jalapeños.
Move the skillet to ensure it is thoroughly coated in melted butter and pour the batter into the skillet. Place 6 jalapeño slices on top.
Bake cornbread in 425°F oven for 15 minutes, then insert a wooden skewer in middle. If it is clean, the cornbread is done baking.
If it has sticky crumbs, bake another 5 minutes.
Cornbread is best eaten warm, with more butter and honey.