Combine flour, cornmeal, thyme, and salt in a food processor and pulse until mixed.

Add butter and olive oil; pulse until the mixture resembles a coarse meal.

Incorporate ice water and lemon juice, pulsing until a dough begins to form.

Transfer the dough to a floured surface and knead briefly to form a cohesive ball.

Press the dough into a tart pan that has been greased or sprayed with cooking spray.

Ensure the dough covers the bottom and sides of the pan evenly.

Prick the bottom of the tart shell with a fork.

Freeze the tart shell for 20 minutes.

Bake the frozen tart shell in a preheated oven at 400°F (200°C) for 20 minutes, until lightly golden.

Remove the tart shell from the oven and cool on a wire rack.

In a medium bowl, combine cherry tomatoes, olive oil, minced garlic, salt, and pepper; toss to coat evenly.

Spread the seasoned tomatoes in a single layer on a baking sheet.

Roast the tomatoes in the preheated oven at 400°F (200°C) for approximately 25 minutes, until slightly charred and shriveled.

Remove the roasted tomatoes from the oven and allow them to cool on the baking sheet.

Brush the bottom of the baked tart shell with Dijon mustard.

In a separate bowl, combine feta cheese, sliced black olives, chopped sun-dried tomatoes, eggs, and milk; whisk thoroughly.

Pour the cheese and egg mixture into the prepared tart shell.

Arrange the roasted tomatoes on top of the filling.

Drizzle any accumulated tomato juices from the baking sheet over the tart.

Sprinkle the remaining feta cheese and fresh thyme leaves over the tart.

Bake the tomato tart in the center of the preheated oven at 400°F (200°C) for 25 to 30 minutes, or until the filling is puffed and browned and the cheese is melted and lightly browned in spots.

Remove the baked tart from the oven and let it cool on a wire rack for at least 20 minutes before serving.

Garnish with fresh basil leaves and serve warm, at room temperature, or chilled.