Peel the onion and cut it in half lengthwise from stem to root. Place one half-onion on a cutting board flat-side down; cut off and discard a thin slice from each end. Cut the rest of the onion into 1/8-inch to 1/4-inch slices. Repeat with the other half.
Put the onion slices into the jar. Arrange the garlic cloves and sprigs of thyme (or rosemary).
Pour the vinegar and water into a small saucepan over medium heat. Add the honey, salt, and peppercorns and warm up while stirring just until the honey and salt blends into brine. Do not boil.
Pour the brine into the jar and cap. At first it will seem like there isn't enough brine (see photo below). Don't worry; the salt draws moisture from the onions and they will soften. After about an hour you'll see that there is plenty of brine to cover the onions. Flip the jar over periodically to help the process.
After the brine cools down, refrigerate. Wait a few hours or until the next day before eating so the flavor has a chance to set in.