Mix ketchup, Worcestershire sauce, wine or water, honey, soy sauce, ginger, and pepper in a small saucepan. Measure out 1/4 cup mixture into a small bowl. This is your reserved glazing sauce. Set aside for glazing meatballs later. Bring remaining mixture to a simmer over medium-high heat, stirring occasionally and reducing heat if needed, until sauce thickens, about 5 minutes. Transfer sauce to a small bowl. This is your reserved glazing sauce.
Place a rack in upper third of oven; preheat to 450F. Line a rimmed baking sheet with foil. Trim broccoli stems and remove from the crown. Peel off the tough outer skin, if needed. Slice crosswise into 1/2-inch pieces. Cut florets into 2-inch pieces. Toss on prepared baking sheet with 1 tablespoon vegetable oil, 1 teaspoon salt, and a few pinches of red pepper flakes (optional). Push to the edges of baking sheet to create a space for meatballs. Brush space with the remaining 1 tablespoon vegetable oil.
Mix chicken, egg, scallions, garlic, ginger, panko, sesame oil, pepper, remaining 1 1/2 teaspoon salt, and 1/8 cup water in a medium bowl. Gradually add more water (up to another 1/8 cup) until the meat mixture is your preferred consistency.
Using wet hands, form into twelve 1 1/2 inch-diameter meatballs. Arrange on baking sheet. Brush with some of the reserved glazing mixture. Bake until meatballs are cooked through, 14–18 minutes. Remove from oven.
Heat broiler. Brush meatballs with remaining reserved glazing mixture. Broil until broccoli is charred and meatballs are browned in spots, about 5 minutes.
Spoon meatballs and broccoli over rice in bowl. Drizzle with reduced glazing sauce and sprinkle with sesame seeds (optional).
