Preheat a Dutch oven over medium heat and add 1 tablespoon of extra virgin olive oil. While the oil heats, season the chuck roast with 1/2 teaspoon fine sea salt and 1/2 teaspoon freshly ground black pepper (using half of each, as the rest will be used for the onions). Carefully place the roast into the Dutch oven and sear it on all sides until well browned. This process takes about 10–12 minutes in total, turning with tongs as needed. Once browned, transfer the roast to a plate and set aside.
While the beef is browning, peel the yellow onions, cut them in half, and thinly slice them (using a food processor with a slicing attachment for convenience, if desired). Add 2 tablespoons extra virgin olive oil to the Dutch oven. Add all of the sliced onions and season with the remaining 1/2 teaspoon fine sea salt and 1/2 teaspoon freshly ground black pepper. Cook the onions over medium heat, stirring frequently, until they are translucent and just starting to soften, about 5 minutes. Then reduce the heat to medium-low and continue cooking, stirring occasionally and scraping the bottom of the pot, for another 20 minutes until the onions are soft and light golden in color. Be careful not to let them burn.
Add the minced garlic and maple syrup (or brown sugar) to the softened onions. Cook, stirring frequently, for another 7–8 minutes until the garlic is softened and the onions are nicely caramelized. Sprinkle the flour over the onions, stirring well to coat. Deglaze the pan by pouring in the red wine (or extra beef stock), scraping up any browned bits from the bottom. Add the beef stock and stir to combine, making sure there are no lumps from the flour. At this stage, I like to taste the sauce and adjust salt if needed for extra flavor.
Return the seared chuck roast (from Step 1) to the Dutch oven, nestling it into the French onion mixture. Make sure the liquid mixture covers most or all of the roast. Add the sprig of rosemary and the bay leaf. Increase the heat to medium-high just until the pot comes up to a simmer, then clamp the lid on. Transfer the Dutch oven to an oven preheated to 300°F. Braise, undisturbed, for 3 hours. Then, carefully remove the pot from the oven, turn the roast over using tongs or forks, and pull it slightly apart into a few large pieces (it should be very tender). Cover and return to the oven for another 30–45 minutes until meltingly tender.
Remove the pot roast from the oven and uncover. Let the roast cool slightly before serving. For best flavor, I like to cool the roast completely and refrigerate it in the same pot, then reheat it for dinner the next day—this really deepens the flavors. When ready to serve, reheat until piping hot. Serve the pot roast with plenty of the rich onion sauce ladled over mashed potatoes, polenta, or buttered egg noodles as desired.