Score duck breast fat with a very sharp knife and sprinkle with sea slat and fresh ground pepper. Place a dry , cold, cast iron pan on your burner, then place the duck breasts in the pan, fat side down. Light the flame and set to medium low. This will begin the fat rendering process and could take up to 20 minutes. As you sear the fat, spoon off the excess grease.
Once the duck fat is sufficiently seared, flip and sauté for and additional 5 minutes until done to your liking (130º for medium rare if you're using a thermometer) Remove from pan and set aside.
Deglaze the pan with 1/2 cup of the sherry. Be careful as the sherry will be very flammable. As it deglazes, turn the flame to low and add the butter. Once the butter has melted add the chopped shallots and cooked until translucent.
Fold in the chopped figs and cook on low for 2 minutes. Then add the chicken broth, cream and sherry.
Add the duck breasts to the pan to coat with the sauce. Warm the duck breast through.
Ladle sauce onto each plate and place a duck breast on each. Sprinkle with toasted almonds and thyme.