About 4 hours before we want to eat, we preheat the oven to 325 degrees F. We slice the onions and chop the garlic on a cutting board. We heat the vegetable oil over medium-high heat in our dutch oven. We take the meat out of the fridge and, using tongs, we take the two pieces of roast out of the bag and place on a plate. We pat them dry and then brown them, one at a time, in the dutch oven on all sides. For the two pieces of meat, this takes about 15 minutes. We pour off the fat in the pan when the meats are browned and reserved on a clean plate. We deglaze the pan with the chicken stock, scraping up the brown bits with a wooden spoon. We put the two meats back in, fitting them in one layer. We cover the meat with the onions and garlic, cover, and put in the oven for 1 hour.
After 1 hour, we take the dutch oven out and place on the stove. We remove the cover (with a pot holder!), and move the two pieces of meat on top of the onions. The liquid level looks good, this is a braising technique after all, and we want the meat to be partially covered with the stock. We cook it for 30 minutes, uncovered, and stir the onions and check the liquid again. We return it to the oven again, uncovered, for another 30 minutes.
Now that 2 hours have passed, we put the cover back on and continue to cook for about another hour until the meat is fork-tender. We take the dutch oven out the oven, turn off the oven, and, using clean tongs, we take out the meat and place in a large bowl. We strain the liquid through a colander into a medium bowl and put the onions into the large bowl with the meat.
On a piece of baguette, we put some of the meat and onions and drizzle a little of the sauce, trying to get the sauce from the bottom of the bowl as the fat is rising to the surface. We refrigerate all the remaining meat and onions (covered with plastic wrap) and the bowl of sauce for a future meal!