Sprinkle cut sides of tomatoes with 1/4 teaspoon pepper and 1/8 teaspoon salt; drizzle with 1 tablespoon olive oil and vinegar. Set aside.
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 peas from water than cook the corn till tender drain and cool. Discard ham hock, onion, and thyme.
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.
Divide tomato slices evenly among 2 plates; top each serving evenly with cherry tomatoes. Spoon 2 heaping tablespoons peas over each tomato stack. Arrange 1/2 cup of corn around the base of tomato stack. Arrange 5 pieces fried okra on each serving; Cross 2 slices of bacon on top of each salad
Combine the remaining 2 tablespoons buttermilk, chives, and garlic in a small bowl. Add remaining 1/8 teaspoon salt, 1/8 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.