In a small saucepan, bring the chicken bone broth to a boil, then add the basmati rice, reduce heat to low, cover, and simmer for 15 minutes until the liquid is fully absorbed.
While the rice cooks, place the slivered almonds in a small dry skillet over medium heat and toast for 3-5 minutes, stirring frequently, until they are golden and fragrant.
Season the chicken breast evenly with half of the sea salt and black pepper.
Heat the olive oil in a skillet over medium-high heat, add the chicken, and cook for 6-7 minutes per side until the internal temperature reaches 165°F.
Remove the chicken from the pan and let it rest on a cutting board for 5 minutes before slicing into thin strips.
Once the rice is done, fluff it with a fork and stir in the minced garlic, lemon zest, lemon juice, chopped parsley, chopped dill, and the remaining salt and pepper.
Gently fold the toasted almonds into the rice pilaf, reserving a few to sprinkle on top.
Serve the sliced chicken over a generous bed of the warm, herb-flecked rice pilaf.