In a medium-sized saute pan over high heat, add 2 tablespoons of olive oil. Add the shallots, garlic and mushrooms and cook until a nice color develops, about 3 to 4 minutes. Stir in the remaining 2 tablespoons olive oil and a splash of balsamic vinegar. Whisk in the beef broth and bring the mixture to a simmer. Cook until the mixture thickens, approximately 3 to 4 minutes. Remove the pan from the heat, then mix in the mascarpone cheese, chives and the salt and pepper.
Add the ground beef and steak seasoning to a medium bowl and mix well. Form the meat into 4 burgers. Put the burgers on the grill and cook for 4 to 6 minutes on each side. Top each with a slice of cheese and cook until the cheese melts, about 1 minute. Remove the burgers from the grill and put on a platter.
Spread the cut sides of the rolls with Dijon mayonnaise blend and top with a burger patty. Sprinkle each burger with a liberal amount of fried onion pieces. Spoon a good amount of creamy mushrooms on top and cover with the other half of the bun. Serve.