Lay puff pastry out on a work surface. Cut 8, 2 1/2-inch-round disks out of the pastry. Place disks on a baking sheet lined with parchment paper. Place a second sheet of parchment on pastry, and top with another baking sheet to weigh down pastry.
Bake at 375° for 12 to 15 minutes or until lightly browned; set aside and cool.
Brush tomato slices and wedges with 1/4 cup olive oil. Sprinkle evenly with thyme, salt, and pepper, and place tomatoes on baking sheets. Bake at 350° for 15 minutes or until tomatoes are soft; cool slightly.
Spread pastry rounds evenly with goat cheese. Using a spatula, carefully stack tomato slices evenly on pastry rounds, and top with tomato wedges.
Toss greens and next 3 ingredients with vinaigrette in a small bowl. Top each tomato tart evenly with salad.
Place tarts on individual serving plates, and drizzle with balsamic vinegar and remaining 1/4 cup olive oil. Sprinkle plates with olives.