To make the arugula pesto: In a food processor, grind the pine nuts and walnuts to a fine powder. Add the garlic, olive oil, arugula, lemon juice, and cheese and purée until blended. Season with salt and pepper.

To make the cherry tomato relish: Cut the cherry tomatoes in half. In a large bowl, whisk the olive oil, balsamic vinegar, garlic, salt, and pepper together. Add the cherry tomatoes and mix gently to coat.

Slice off the ends of the green tomatoes and cut each tomato into three 1/2-inch-thick crosswise slices. Pour the buttermilk into a shallow bowl. In a second shallow bowl, mix the panko, cornmeal, flour, cheese, chipotle powder, paprika, the 1 teaspoon salt, and the 1 teaspoon pepper together. Dip the tomato slices into the buttermilk, then into the panko mixture, patting the mixture onto the tomato slices to make sure it adheres.

In a deep, heavy sauté pan, heat the canola oil to 350°F. Add the green tomatoes and fry until golden brown, about 1 minute per side. Using a slotted spatula, transfer to paper towels to drain. Season with salt and pepper.

To serve, place 3 tomato slices and a spoonful of relish on each of 6 salad plates and drizzle with 2 tablespoons of the pesto.