To begin the dressing, placed minced tarragon in a bowl, and add Dijon mustard. Add a pinch of grey salt, sherry vinegar, and olive oil. Whisk mixture together thoroughly.
In a large bowl, toss the greens with enough of the dressing to coat them lightly. Taste and adjust the seasoning. Set aside.
For eggs, make sure that upon starting they are room temperature. Bring the water to a boil in a deep saucepan. Add the wine vinegar and salt. Adjust the heat so the water barely bubbles. One at a time, break the eggs into a custard cups or small bowl, then slide gently into the water. Allow eggs to cook for about 1 1/2 minutes, then, with a slotted spoon, gently lift and shape the whites around the yolks. Continue to cook until the whites are just set and the yolks are glazed but still liquid about 2 1/2 minutes longer. Transfer the poached eggs with a slotted spoon to a clean dish towel or paper towels to drain.
Place poached eggs on top of coated greens in large bowl, add a pinch of salt, to taste, and top with about 3 tablespoons or more of the prosciutto bits.
Note: Eggs poach best when the water is relatively deep, so use a deep saucepan. Adding vinegar to the water helps to set the whites.
TIP: The best way to make these bits is with the shanks of prosciutto. Ask your local butcher to save those shanks, and grind them on the medium grind if you want to save some chopping, or dice it finely yourself. Shank should cost about half of sliced prosciutto, as the store probably has no use for it.
Note: Whether you are chopping the prosciutto by hand or putting it through a meat grinder, you'll have an easier time if the prosciutto is partially frozen.
Place prosciutto in heated pan. Drizzle bits with olive oil, and cook, stirring. The prosciutto will give off steam for about 5 minutes while it releases its moisture. When the hiss of steam turns to a sizzle, turn the heat down to medium and cook, stirring occasionally, until the prosciutto bits are crisp, about 30 minutes. Using a slotted spoon, transfer the bits to several thicknesses of paper towel to drain. The bits will crisp even more as they cool. Use immediately or freeze the bits for up to 6 months and warm in a skillet as needed.