For the cornbread croutons: Preheat the oven to 325 degrees F.
Grease a baking sheet with 2 tablespoons of the butter. Gently arrange the cornbread cubes on the baking sheet and drizzle with the remaining butter. Season with salt and pepper. Don't toss the cornbread or it will crumble.
Toast, gently turning halfway through, until golden brown, 16 to 18 minutes. Allow it to cool 5 to 7 minutes before moving to a serving platter.
For the vinaigrette: Put the blueberries, champagne vinegar, honey and lemon zest and juice in a small saucepan over medium heat. Bring to a low simmer and cook until thickened slightly, about 5 minutes. Let cool slightly.
Transfer the blueberry mixture to a blender and puree at low speed. Increase to medium and slowly drizzle in the oil, allowing it to emulsify. Season with salt and pepper. Pour into a pitcher or container. If making ahead, the vinaigrette can be made up to 48 hours in advance and refrigerated in an airtight container. Shake to emulsify if separated.
For the salad: To assemble on a platter, layer half the arugula, half the croutons and half the tomatoes, then repeat with the remaining arugula, croutons and tomatoes. Top with the blueberries and goat cheese. Drizzle with the vinaigrette and top with the torn basil.
Preheat the oven to 450 degrees F.
Stir together the cornmeal, flour, baking powder and salt in a bowl.
Measure the buttermilk and milk into a measuring cup and add the egg. Stir together with a fork. Add the baking soda and stir. Pour the milk mixture into the dry ingredients. Stir with a fork until combined.
In a small bowl, melt 1/4 cup shortening in the microwave. Slowly add the melted shortening to the batter, stirring until just combined.
In a cast-iron skillet, melt the remaining 2 tablespoons shortening over medium heat. Pour the batter into the hot skillet. (The batter should sizzle.) Spread to even out the surface. Cook on the stovetop for 1 minute, and then transfer to the oven and bake until golden brown, 20 to 25 minutes. The edges should be crispy!
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.