In a small pot over medium heat, add the reserved cooking liquid and cook until it is hot.
Add the canola oil to a saute pan over medium heat. Add the onions and cook 20 minutes on medium-low to caramelize.
Butter 1 side of each slice of bread. Layer the beef, onions, and cheese evenly over the plain side of 4 bread slices. Top each with the other 4 slices of bread, buttered-side up.
Heat a grill pan over medium-high heat and grill the sandwiches until golden brown on both sides and the cheese is melted, 4 to 5 minutes per side.
Serve the sandwiches with the hot beef jus for dipping.