Preheat the oven to 325°F.
To peel the pearl onions, bring a few inches of water to a boil in a medium-sized pot. Fill a medium-sized bowl with ice water and set it aside. Add the onions and turn off the heat. Let them sit for about two minutes, drain them, and then add them to the bowl of ice water. Once they are cool enough to touch, use a paring knife to cut a sliver off where the root is. Then use your hands to gently slide the skin off. Set the peeled onions aside.
Trim the fat off the brisket and season both sides with salt and pepper. Set aside.
Coat the bottom of a large, oven proof pot with a fitted lid, with olive oil. (A Dutch oven in perfect.) Place the pot over medium-high heat.
Once the pot is very hot, add the brisket. You should hear a sizzling sound when it hits the pan -- if you don't, wait until it's hotter. Sear the brisket until it's nicely browned, 1 to 2 minutes per side.
Remove the brisket from the pot and place it on a large plate. Set aside.
Turn the heat under the pot to medium and add the peeled onions and garlic. Sauté, stirring periodically, until the onions are beginning to brown, about 5 minutes. Add the thyme and continue to cook for another 30 seconds or so, until it's very aromatic.
To deglaze, add the stock, frozen (thawed) blueberries and red wine. Use a wooden, flat-edged spatula to scrape off any bits of brisket, onion and garlic that may be stuck to the bottom of the pot.
Return the brisket to the pot and bring to a boil.
Cover and place in the preheated 325°F oven to braise for 1-½ hours, gently braising any portion of the brisket that's not submerged in the liquid.
Remove the pot from the oven, add the balsamic vinegar, and gently mix it in evenly around the brisket.
Cover the pot again and return it to the oven. Continue to braise until the brisket is very tender, about 1 more hour. (You can test it with a fork to see how easily it comes apart -- you want it to be able to pull apart, but still be firm enough to slice.)
Remove the brisket and place it on a large plate to cool.
Place the pot over low heat and simmer until it's reduced by at least half, and has thickened into a rich sauce, about 30 minutes. As it's simmering, you can use a large soup spoon to remove any grease that rises to the top.
Add the butter and brown sugar and season to taste with salt and pepper. While the sauce is simmering, slice the brisket against the grain, into thin slices, about ¼to ½-inch.
Just before you're ready to serve, fold the fresh blueberries into the sauce.
To serve, either add the brisket slices to the sauce, or arrange the slices on serving platter and drizzle the sauce over them.
Garnish with fresh thyme sprigs.