Mix the sauce ingredients in a small bowl and set aside until ready to use.
Preheat the oven to broil on high.
Cut the bread slices into small rectangles, trying to mimic the size of the filet slices.
Spread the butter evenly on both sides of the bread. Broil the bread for about 3-5 minutes per side to brown. Remove from oven.
Spread about a tablespoon of the mayo mixture onto one side of each bread.
Heat a little vegetable oil in a heavy bottom frying pan on high heat.
Season the filets with salt and pepper on both sides. Add them to the pan.
Cook about 1 minute on each side to brown the outside and cook to rare on the inside.
Place a filet on 4 of the pieces of bread. Top with the remaining 4.
Meanwhile, turn the pan to medium heat and add the balsamic. Stir, scraping the bottom of the pan to get all the bits from the pan into the sauce. Add in the worcestershire and honey and stir to combine. Cook 3 minutes until slightly thickened. Remove from pan.
Cut the sandwiches in half and line them up on a serving plate cut side up. You can use toothpicks if the sandwiches don’t stay together on their own.
Top with chives and a drizzle of the pan sauce before serving.