Place 1 teaspoon of the olive oil in a large skillet over medium high heat.
Add the garlic and cook for about 1 minute.
Add the white part of the leek.
Cook for about 10 minutes until the leek has softened.
Remove from the heat and let cool slightly.
Place the leek and garlic mixture in a blender or food processor.
Add the goat cheese, mustard, and tarragon. Process until smooth.
Remove to a bowl and fold in the pistachios until blended.
Place in the refrigerator and chill thoroughly.
Place each chicken breast between two sheets of plastic wrap.
Pound lightly with a meat mallet or the bottom of a small sauce pan until the chicken breast is about 1/8 inch thick.
Remove one side of the plastic wrap and place the slices of prosciutto on the chicken breast, starting at the center with the ham covering only half of the chicken breast, and the other half of the ham overlapping onto the plastic wrap with no chicken underneath. The result should look something like two circles intersecting. This is so the ham will overlap the line where the chicken comes together when you roll it to help seal the ballotine.
Place the plastic wrap back on top of the chicken and ham, turn the chicken breast over, and remove the other piece of plastic wrap.
Place half of the leek mixture in the center of each chicken breast in a log shape.
Roll the chicken breast around the leek mixture like a burrito, tucking the ends of the breast in to seal the leek mixture inside. The prosciutto will wrap around the chicken to seal the ballotine.
Roll plastic wrap around the chicken breast cylinder to seal tightly and twist the ends (like a Tootsie Roll).
Place each chicken package inside its own small ziplock bag, then put the ballotines in the freezer for 15 minutes.
While the chicken is chilling, place the water in a large saucepan over high heat.
Add the ballotines, inside the ziplock bags, to the water and cook for 8 minutes. Remove and unwrap.
Heat the remaining 2 teaspoons olive oil over medium high heat and add the ballotines.
Cook for about 2 minutes on each side, until the prosciutto is golden brown, and serve.