1. Prepare Ham and Grits: Sauté diced ham in a small skillet over medium heat 3 to 5 minutes or until lightly browned. Drain on paper towels.
2. Bring cream, next 2 ingredients, and 3 cups water to a boil in a medium saucepan over high heat. Gradually whisk in grits; return to a boil. Reduce heat to low; cook, whisking often, 5 minutes or until thickened. Stir in garlic, ham, and 1 cup Gouda cheese; cook, stirring occasionally, 1 to 2 minutes or until cheese melts. Spread in a lightly greased 13- x 9-inch pan; cover and chill 4 hours or until set.
3. Prepare Tomato Gravy: Sauté onion and garlic in hot oil in a 3-qt. saucepan over medium heat 2 to 3 minutes or until tender. Stir in tomatoes and 1 cup water. Bring to a boil, stirring constantly and crushing tomatoes with spoon. Reduce heat to low, and simmer, stirring occasionally, 15 to 20 minutes or until slightly thickened. Stir in basil and next 3 ingredients.
4. Prepare Poached Eggs: Add water to depth of 3 inches in a large saucepan. Bring to a boil; reduce heat, and maintain at a light simmer. Add vinegar. Break eggs, and slip into water, 1 at a time, as close as possible to surface. Simmer 3 to 5 minutes or to desired degree of doneness. Remove with a slotted spoon. Trim edges, if desired.
5. Assemble: Preheat oven to 375°. Invert chilled grits onto a cutting board. Cut into 12 (3-inch) squares; place in a single layer, overlapping slightly, in a 13- x 9-inch baking dish. Spoon gravy over grits. Bake 20 minutes or until thoroughly heated. Top with remaining 1/2 cup Gouda and poached eggs.