Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Remove the puff pastry from the refrigerator 10 minutes before using to make it more pliable.
Slice the tomatoes into 1/4-inch rounds and place them on paper towels. Sprinkle with 1/2 teaspoon of salt and let them sit for 15 minutes to draw out excess moisture. After 15 minutes, pat the tomatoes dry with additional paper towels.
Gently roll out the puff pastry on a lightly floured surface to about 10x14 inches. Transfer to your prepared baking sheet. Using a sharp knife, score a 1-inch border around the edge of the pastry (don't cut all the way through). Prick the inner rectangle repeatedly with a fork.
Spread the Dijon mustard evenly across the inner rectangle of the pastry.
Crumble half the cheese over the mustard layer. Arrange the tomato slices in an overlapping pattern. Sprinkle with minced garlic, thyme leaves, salt, and pepper.
Top with the remaining cheese. Brush the border with beaten egg for a golden finish, and drizzle the entire tart with olive oil.
Bake for 25-30 minutes, or until the pastry is golden brown and the tomatoes have slightly caramelized. The internal temperature should reach 165°F for optimal texture.
Allow the tart to rest for 10 minutes before slicing. If desired, drizzle with balsamic glaze before serving.