Season the chicken breast evenly on both sides with sea salt and black pepper.
Heat the avocado oil in a large non-stick skillet over medium-high heat.
Place the chicken in the skillet and cook for 6 to 7 minutes per side until the internal temperature reaches 165 degrees Fahrenheit.
While the chicken is cooking, steam the broccoli florets in a steamer basket over boiling water for about 4 to 5 minutes until tender-crisp.
In a small bowl, whisk together the honey, coconut aminos, and sesame oil until well combined.
During the last 2 minutes of chicken cooking, pour the honey mixture into the skillet, turning the chicken frequently to coat it in the thickening glaze.
Remove the skillet from the heat once the glaze is sticky and reduced.
Serve the glazed chicken over a bed of warm jasmine rice with the steamed broccoli on the side.
Garnish the chicken with the sliced almonds to provide a crunchy texture to every bite.