In a medium saucepan, melt 2 tablespoons butter over medium heat. Add the shallot and cook, stirring, until translucent, 1 to 2 minutes. Add the cornstarch and cook for 1 minute. Whisk in the beef broth.
Add the roast beef to the sauce and warm over low heat.
Preheat a nonstick grill pan over medium heat. Spread the remaining 2 tablespoons butter on the split sides of the baguette sections. Using tongs, top half the sections with the warm roast beef, reserving the sauce. Top with the cheese and the remaining baguette sections. Place the 4 panini on the hot pan. Weigh down with a heavy skillet and cook for 2 minutes, then flip the panini and cook for 2 minutes longer.
Remove the panini from the heat and divide the sauce among 4 small bowls for dipping.