Bring a large saucepan of salted water to a boil. Add the broccoli and cook, stirring, until bright green and crisp-tender, about 3 minutes. Use a slotted spoon to transfer to a large bowl. Add the rice noodles to the water and return to a boil. Remove from the heat and let soak while you prepare the chicken, stirring occasionally.
Combine the sugar and 1 tablespoon water in a large skillet over medium-high heat, stirring until the sugar dissolves. Cook, undisturbed, until the mixture is dark amber, about 3 minutes. Carefully stir in the vegetable oil and garlic and cook until the garlic is golden, about 30 seconds. Add the chicken and fish sauce and cook, stirring, until the chicken is no longer pink, about 2 minutes. Remove from the heat and stir in the chile pepper, cilantro and 1/4 teaspoon pepper.
Drain the noodles and add to the bowl with the broccoli. Add the scallions and chicken and toss. Divide among plates and top with more cilantro and scallions.