In a large bowl, combine flour, cornmeal, sugar, and salt. Cut in the butter using a pastry blender until no visible large chucks remain. (It’s often good to switch to using your fingers part way through.) Add olive oil and water and mix until dough comes together. Shape dough into a disk, wrap in plastic, and refrigerate for at least 1 hour.
Preheat oven to 375º. Line a large baking sheet with parchment paper.
Place tomato slices on paper towels for 5 minutes to soak up excess liquid. Sprinkle with salt and pepper.
In a small bowl, mix together cream cheese and roasted garlic. Add half of the feta cheese. Set aside.
Place dough on a lightly floured surface. Roll dough out, lifting and rotating the dough every few rolls so that it doesn’t stick to the surface. Use more flour if necessary. Once dough is 14 to 15 inches across, move it to the baking sheet.
Spread cream cheese mixture on the dough leaving a 2-inch border. Place tomato slices on top, overlapping them some. Fold dough inward, covering the edges of the tomatoes and pinching together any tears in the dough. Sprinkle with remaining feta cheese and pepper and place thyme sprigs on top. Using a pastry brush, coat top of dough with egg. (I forgot to brush mine with egg :( )
Bake for 40 minutes and cut into slices to serve.