Preheat your oven to 400°F and line a small baking sheet with parchment paper.
Rinse the jasmine rice in a fine-mesh sieve under cold water until the water runs clear to remove excess starch.
In a small saucepan, combine the rinsed rice with 0.5 cup of water, bring to a boil, then reduce heat to low and simmer covered for 15 minutes.
While the rice cooks, pat the chicken breast completely dry with a paper towel to ensure a good sear.
In a small bowl, mix the olive oil, minced garlic, finely chopped rosemary, lemon zest, sea salt, and black pepper.
Rub the herb mixture evenly over both sides of the chicken breast and place it on the prepared baking sheet.
Roast the chicken for 18 to 22 minutes, or until the internal temperature reaches 165°F.
During the last 6 minutes of roasting, steam the broccoli florets in a steamer basket over boiling water until they are vibrant green and tender-crisp.
Remove the chicken from the oven and let it rest for 5 minutes before slicing to keep the juices intact.
Fluff the cooked rice with a fork, stir in the fresh lemon juice, and serve the sliced chicken on top with the steamed broccoli on the side.