Heat a gas grill to medium or prepare a medium-hot charcoal fire. (Or heat the broiler to high.) Set the tomato slices on a small rack set over a rimmed baking sheet and sprinkle with 1 Tbs. of the oil, the thyme, red pepper flakes, and 1 tsp. kosher salt. Let sit at room temperature for at least 10 minutes or up to a couple of hours.
Brush both sides of the bread with the remaining 3 Tbs. oil. Sprinkle lightly with salt. Grill (or broil) until crisp with prominent grill marks (or nicely browned), about 2 min. Flip and cook the other side in the same manner. Transfer to a platter and let cool to room temperature (they can sit for up to 2 hours, loosely covered).
Pour the tomato juices from the baking sheet into a small bowl. Before serving, brush these juices on the bread. Top with the tomatoes and a drop or two of balsamic vinegar and serve.
nutrition information (per serving):
based on eight servings;
Photo: Scott Phillips