Spread sesame seeds in a small skillet over medium-high heat and cook, stirring constantly, until lightly toasted and beginning to release oil, about 1 minute. Remove to a plate to cool.
Warm vegetable oil with sesame oil in a large skillet over medium-high heat. Add garlic and sauté until fragrant, about 1 minute. Stir in bell pepper. Add broccoli and stir well until coated in oil. Cook, stirring, until broccoli is slightly softened, 2 to 3 minutes.
Pour in broth; bring to a simmer. Reduce heat to low, cover and cook, stirring once or twice, until broccoli is tender, about 5 minutes. Sprinkle with sesame seeds. Season with salt and pepper; serve warm.