Prepare a medium-high grill fire. Grill the bell peppers, turning occasionally, until the skin chars all over, 15 to 20 min. Put the charred peppers in a heatproof bowl, cover with plastic wrap, and let sit until cool enough to handle, about 30 min.
Meanwhile, in a large bowl, combine the balsamic vinegar, olive oil, 1/2 tsp. of the thyme, salt, and about 5 grinds of pepper. Mix well.
Remove the pepper skins and seeds and cut the peppers into thin strips. Add the peppers to the vinegar mixture and let them marinate for at least 1 hour and up to 3 days. (Refrigerate if making more than a few hours ahead and return to room temperature before assembling the crostini.
Spread each slice of the grilled garlic bread with a generous layer of goat cheese, sprinkle with some of the remaining thyme, and top with a tangle of the peppers and a small grind of black pepper. Serve immediately.