With a boning or utility knife, cut a slit in one side of each chicken breast to create a pocket about 3-4 inches long, taking care not to slice through to the other side.
In a small bowl, combine 1/4 cup toasted almonds with goat cheese and apricots. Stuff each breast with 1/4 of the mixture then press on top of chicken to close. Season on the outside of the breasts with kosher salt and fresh ground black pepper.
Preheat oven to 375F. Place a large oven-safe skillet on the stovetop, and heat olive oil over medium heat. Cook chicken until golden brown, about 3 minutes on each side, browning the presentation side first. Place skillet in preheated oven for about 10 minutes, or until chicken is cooked through.
Remove chicken from skillet and place it on a cutting board. Cover with foil to keep warm. Put skillet back on the stovetop on medium heat, and add 1 cup chicken broth, scraping the bottom of the pan to remove the browned bits. If using flour to thicken, mix with a little cold water or room temperature stock. Add flour mixture to the broth, whisking to avoid lumps. Cook for 1 minute and then whisk in the apricot preserves and more broth if needed. Cook for a minute to thicken and then add the rosemary. Adjust seasoning if necessary.
Slice chicken in half and place on serving plate. Top with apricot pan sauce and the remaining toasted almonds for garnish and serve immediately.