Place the scallops on a plate or platter and put in the refrigerator, uncovered, for 30 minutes.
In a small saucepan. melt the butter over medium heat.
Add the scallions and a small pinch of salt, reduce the heat to low, and cook 15-20 minutes, until the scallions are very soft.
Sprinkle the flour over the scallions, and continue to sauté for a minute or two. Cooking the flour for a couple of minutes will get rid of any flour taste in your sauce. You want the flour to thicken, not flavor, your sauce.
Slowly add the milk. Raise the heat to medium, and cook, whisking constantly, until thickened. This should take around 5 minutes.
Add the tarragon leaves and stir through, then turn off the heat and pour the mixture into a blender.
Puree until completely velvety smooth, then return to the pan over low heat, cooking until the mixture is thick enough to coat the back of a spoon.
Be sure to keep your pan on very low heat. You may need to take your pan on and off the heat, stirring continually, until the sauce thickens.