For the vinaigrette, drain and roughly chop the green peppercorns. Place them in a steel mixing bowl with the vinegar. Whisk in the olive oil, and then the honey. Place the mixture in a small sauce pot with the tarragon and warm over medium heat. Do not boil. Cook for about 5 minutes. Remove from heat and cool.
For the steaks, season heavily with salt and fresh cracked pepper. Warm 1 tablespoon of vegetable oil in a heavy bottom pan. Pan sear the steak on each side for about 4 minutes. Add 3 tablespoons whole butter, 1 bay leaf and chopped shallots to the pan and baste the steaks with the browning butter. Remove the pan once the steaks are at the desired temperature.
For the vegetables, peel and then cut (if necessary) the vegetables to similar sizes. In a heavy bottomed skillet gently brown the vegetables until golden brown and tender. Season with salt and pepper.
To serve place the steak on a large dinner plate. Add some of the vegetables, and finally, spoon some of the vinaigrette over the beef and vegetables. Serve immediately.