Heat 1 Tbsp. of oil in saucepan. Add sliced onion and cook until browned. Remove from heat and add red wine vinegar. Set aside.
Combine mayonnaise, blue cheese and horseradish in a small bowl.
Preheat panini press.
Spread each slice of bread with some mayonnaise mixture. Evenly distribute roast beef and sauteed onions on 4 slices of bread. Top with slice of bread.
Spread 1 Tbsp. oil on heated panini press. Place sandwiches on press and cook until golden brown.
If you do not have a panini press, use a non-stick skillet and weigh down the sandwiches with a Dutch oven.