Heat the oil in a Dutch oven or large pot over medium-high heat until hot. Sprinkle all sides of the beef with salt and pepper, and then add to the pot. Sear the beef, turning with tongs until all sides are evenly browned, about 12 minutes. Transfer the beef to a plate.
Add the garlic and onions to the pot and cook until soft and slightly browned, stirring occasionally, about 6 minutes. Stir in the flour until it coats the onions, about 30 seconds, then pour in the beer, scraping the bits off the bottom of the pot. Add the beef stock, mustard, bay leaves and 1 teaspoon salt and return the beef to the pot. Bring up to a boil, then reduce to a simmer and cover with a lid. Simmer until the meat is very tender and falling apart, about 3 hours, stirring occasionally to prevent sticking.
Heat the oven to 425 degrees F.
When the meat is almost tender, spread the fries onto a baking sheet and cook according to manufacturer's instructions until crispy.
Remove the meat from the liquid, and let cool slightly before shredding with a fork. Discard the bay leaves from the pot. If the liquid is thin and soupy, bring to a simmer over medium heat and cook until reduced to a gravy and almost thick enough to coat a spoon, about 15 minutes. Return the shredded meat to the pot.
To assemble the sandwiches, place a handful of French fries on the bottom of each roll, having some of them hang off the edge. Top with a heaping 1/3 cup of the cheese and 1 cup shredded meat. Ladle 1/4 cup extra gravy over, and top with the bun.