To prepare jam, arrange the cherry tomatoes in a single layer on a jelly-roll pan. Broil for 20 minutes or until browned, stirring occasionally.
Heat 1 tablespoon of olive oil in a medium saucepan over medium-high heat. Add the onion, apple, and ginger; sauté 5 minutes or until tender. Add sugar; cook 1 minute. Add tomatoes, water, and the next 4 ingredients (through pepper), and bring to a boil. Reduce heat, and simmer until reduced to 2 cups (about 45 minutes). Remove from heat; cool.
Preheat oven to 400º.
To prepare shortcakes, lightly spoon flour and cornmeal into dry measuring cups; level with a knife. Combine flour, cornmeal, baking powder, and 1/4 teaspoon salt in a large bowl, stirring with a whisk. Make a well in center of mixture. Combine milk, oil, and juice; add to flour mixture. Stir just until moist. Turn dough out onto a lightly floured surface; knead lightly 3 or 4 times. Roll dough into a 1/2-inch thickness. Cut with a 2 1/2-inch round cutter into 12 rounds; place on a baking sheet coated with cooking spray. Bake at 400º for 15 minutes or until lightly browned. Serve with jam.