Season the salmon flesh and skin with salt and pepper.
Heat a large sauté pan over moderate heat and coat with oil.
Place the salmon into the pan, skin-side down, and cook the salmon for 2-3 minutes.
Check the salmon skin, add 1 tablespoon of butter, and continue cooking for 3-4 minutes until the skin is a beautiful brown color.
Reduce the heat to low, and add the white wine and 1/3rd of the sliced garlic.
Tilt the pan, so the salmon is slightly raised from the heat, and the liquid is in direct contact with heat. Use a spoon and continuously baste the hot garlic wine liquid over the top of the salmon to cook the flesh.
Continue this process for 4-5 minutes, until the salmon's flesh is cooked, but still tender.
NOTE: if you are uncomfortable with this step, you can place the salmon into a 350-degree Fahrenheit oven for 4-5 minutes, after the skin has been browned, to finish cooking the salmon.
Remove the salmon from the pan and reserve.
Turn the heat back up to moderate, to have the liquid come to a boil. Turn off the heat, add 2 tablespoons of butter, and continuously stir until the butter has fully melted into the sauce.
Add the tarragon, lemon juice, and season to taste with salt and pepper.
Remove the sauce from the pan to a vessel and wipe the pan clean. Reserve the sauce for the salmon.