Preheat oven to 375 degrees Fahrenheit. Line 1-2 baking sheets with parchment paper.
Mix balsamic vinegar, coconut oil, ginger, lemon juice, and salt and pepper in a small bowl. Place brussels in a large bowl. Add balsamic mixture and stir until combined. Place on baking sheets, spreading them out evenly, and roast for 30 minutes, stirring halfway through.
Place in a serving bowl and add pomegranates and lemon zest. Mix well.