1. Preheat oven to 375°.
2. Arrange tomato halves, cut side up, on a baking sheet. Drizzle tomatoes with 1 teaspoon oil; sprinkle with 1/4 teaspoon pepper. Bake at 375° for 1 hour and 30 minutes or until tomatoes are soft and have lost a lot of their moisture.
3. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and baking powder in a medium bowl. Add milk and egg; stir until smooth. Stir in remaining 1/4 teaspoon pepper, corn, green onions, and salt.
4. Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Drop batter by level tablespoonfuls into pan to make 6 fritters; cook 2 minutes or until tops are covered with bubbles and edges are golden. Carefully turn fritters over; cook 2 minutes or until golden. Repeat procedure with remaining 1/2 teaspoon oil and remaining batter.
5. Combine mayonnaise, juice, garlic, and water. Place 1 fritter on each of 4 plates. Top each with 1 tomato half and 1/2 cup arugula. Repeat layers with remaining fritters, tomato halves, and arugula, ending with fritters. Top each serving with 1 prosciutto slice; drizzle with 4 teaspoons aioli.