Slice the mushrooms into 1/2-inch slices or quarter them. If using large mushrooms like portobello, cut them into 1-inch slices lengthwise and then again crosswise, so you have about 1-inch dice-sized pieces.
Place the mushrooms in a large sauté pan over medium-high heat. Add 1/4 cup of water to the pan and let the mushrooms cook for about 8 minutes, until they are softened and have released their liquid. Once the water has evaporated, add the olive oil, minced garlic, and salt. Stir and let the mixture cook for five minutes.
Add the balsamic vinegar, scraping up any brown bits from the bottom of the pan. Add two sprigs of rosemary and 3 sprigs of thyme. Let the mixture cook for an additional 15 minutes over medium-high heat. If the mushrooms get too dry, add about 1/4 cup of water, and again scrape up any brown bits from the bottom of the pan.
Remove the sprigs of herbs from the pan. Season the mushrooms with pepper, the remaining minced thyme leaves, and about one teaspoon of minced rosemary. Taste and add extra salt or a splash of balsamic if needed.
Notes
You can prepare these mushrooms in advance and keep them in the refrigerator for up to three days. Reheat them in a pan over medium heat, or in the microwave. You can't overcook mushrooms, so you can keep them warm over low heat, adding about 1/4 cup of water if they dry out, and then letting the liquid cook off, until ready to serve.