1. Sprinkle cut sides of tomatoes with 1/2 teaspoon pepper and 1/4 teaspoon salt; drizzle with 1 tablespoon olive oil and vinegar. Set aside.
2. Combine peas, ham hock, onion, and thyme in a medium saucepan; cover with cold water. Bring to a simmer over medium heat; simmer 15 minutes or until peas are just tender, stirring occasionally. Remove from heat; drain and cool. Discard ham hock, onion, and thyme.
3. Clip a candy/fry thermometer onto the side of a large skillet; add 2 cups peanut oil to pan. Heat peanut oil to 350°. Place 1/4 cup buttermilk in a shallow dish. Combine flour, cornmeal, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a shallow dish, stirring well. Dip okra in buttermilk; dredge in flour mixture. Place okra in hot oil; fry 2 minutes or until golden, making sure oil temperature remains at 350°. Remove okra using a slotted spoon; drain on paper towels.
4. Divide tomato slices evenly among 6 plates; top each serving evenly with cherry tomatoes. Spoon 2 heaping tablespoons peas over each tomato stack. Arrange 5 pieces fried okra on each serving; sprinkle evenly with bacon.
5. Combine the remaining 2 tablespoons buttermilk, chives, and garlic in a small bowl. Add remaining 1/4 teaspoon salt, 1/4 teaspoon pepper, and juice; stir well with a whisk. Gradually add remaining 1 tablespoon olive oil, while whisking vigorously. Stir in crème fraîche. Drizzle 2 tablespoons dressing mixture over each serving; top with 1 tablespoon basil.