Heat a large skillet over medium. Add sesame seeds and toast, tossing, until golden, about 3 minutes. Transfer to a small bowl.

Return skillet to heat and add vegetable oil. Add broccolini, garlic, ginger, and water. Cover and cook, stirring occasionally, until broccolini is crisp-tender, about 12 minutes. Add soy sauce and cook until it evaporates, 30 seconds. Top with sesame oil and sesame seeds.