Pat the beef cubes thoroughly dry using paper towels. Generously season the beef pieces all over with kosher salt and freshly ground black pepper. This step is crucial, as seasoning at this early stage helps to develop flavor throughout the entire stew.
Heat half of the olive oil in a Dutch oven over high heat until shimmering. Working in batches and avoiding overcrowding, sear the seasoned beef cubes on all sides until they are well browned. Refrain from moving the meat too often to promote even browning. Add more oil as needed for additional batches. As the beef finishes searing, transfer the browned pieces to a plate. I always let the beef get a really dark crust at this stage—it makes the stew extra rich.
Reduce the heat to medium-high and add the onions and any remaining olive oil to the Dutch oven. Cook, stirring occasionally, until the onions are softened and just turning golden, about 10 minutes. Sprinkle the flour over the onions and stir well, letting it cook and thicken the onions for 4 to 5 minutes. Pour in the Burgundy wine and use a wooden spoon to scrape up all the flavorful browned bits (fond) stuck to the bottom of the pot.
Once the wine comes to a boil, return the seared beef and any accumulated juices to the pot. Add the carrots, garlic clove, and the bouquet garni. Pour in 1 1/2 cups of water (and demi-glace if using) and bring the mixture to a boil. Reduce the heat to medium-low and simmer uncovered, skimming off any foam or oil that rises to the surface. Continue cooking for 2 to 2 1/2 hours, stirring every 15–20 minutes and scraping the pot bottom to prevent scorching. As the stew simmers, add more water in 1/4 to 1/2 cup increments as needed, up to a total of 2 1/2 to 3 cups, to keep the liquid level sufficient and create a rich sauce as the onions break down.
When the beef is perfectly tender and the onions have melted into a thick, savory sauce, remove and discard the bouquet garni. Taste and adjust the seasoning with additional salt if desired. Transfer the stew to serving dishes and garnish with the chopped fresh parsley. I like to add the parsley just before serving for a fresh burst of flavor and color.