To make the balsamic glaze, in a very small saucepan heat the balsamic vinegar and brown sugar over medium heat until it reduces by about one-third (this can happen quickly for such a small amount of vinegar–keep an eye on it). Let cool. It should be syrupy. If it’s too thick, dilute with a tiny bit of balsamic vinegar. If it’s too thin, boil it down a bit more. Set aside. Alternatively, you can use store-bought balsamic glaze.
Preheat the oven or toaster oven to 350 degrees F. Place the garlic cloves on a small piece of aluminum foil and drizzle with a tiny bit of olive oil. Wrap the garlic cloves with the foil and roast for 30 to 40 minutes until tender (open the foil and poke with a fork–it should be completely fork-tender). Remove from the oven and remove the skins from the garlic cloves–they should slip right off.
Add the roasted garlic cloves to a medium mixing bowl and mash with a fork until smooth. Add the goat cheese, 1 tablespoon of the basil, and the thyme, and mix with a rubber spatula until smooth. Season to taste with salt and pepper.
Snip the corner from a 1-quart plastic bag (or snip the tip of a small pastry bag) to make a 1/2-inch wide opening. Transfer the goat cheese mixture to the bag. Pipe equal amounts of the cheese mixture into the peppers. The peppers can be covered and refrigerated for up to 1 day. Bring to room temperature before heating.
Position the broiler rack about 8 inches from the source of heat and preheat the broiler on high.
Put the bread slices on a broiler pan and toast them in the broiler, turning occasionally, until golden, about 3 minutes. Arrange the toast on a serving platter. Turn off the broiler.
Put the stuffed peppers in a flameproof baking pan and transfer to the turned-off broiler. Heat the peppers just until they are warm and plump, about 3 minutes (you can also heat them very quickly in a 350 degree F oven if the leftover heat from the broiler isn’t warming them through, just be careful not to overheat them or the cheese will melt).
Using kitchen tongs (let’s be real, I used clean fingers), carefully top each toast with a pepper, taking care not to squeeze the filling out of the pepper. Sprinkle with the remaining 1 tablespoon basil and finish with a drizzle of the balsamic glaze. Serve immediately.