Preheat the oven to 350º. Season the filet on both sides with the salt and garlic salt.
Add oil to a heavy bottom sauté pan and heat over medium to high heat. Place the filet in the oil and sauté for four to five minutes on both sides.
Place into the oven for about 11 minutes for medium well.
In a medium saucepan, place the water along with a pinch of salt over high heat. Bring to a boil then add the lobster and cook for seven minutes. Remove the lobster and split. Serve with the filets.
Place the vinegar, lemon juice, wine, water, ½ the tarragon, shallots, and pepper in a saucepan and bring to a boil over high heat. Reduce the mixture down for fifteen minutes. Strain and set aside.
Place the egg yolks in a medium glass bowl and add the strained liquid. Slowly whisk in the butter in very small amounts with the bowl in a double boiler over very low heat.
Once the butter is whisked in, season with a pinch of salt, then add the remaining tarragon ladle over the lobster and steak.