Preheat oven to 425 degrees F. In a mini food processor, pulse garlic and crackers into crumbs. In a medium skillet, heat 2 tablespoons of the oil. Add the crumb mixture and cook over moderate heat, stirring until crisp and golden, about 5 minutes. Let cool.
In a medium bowl, toss the broccoli with the remaining 1/4 cup olive oil and season with salt. Spread the broccoli on a baking sheet and roast for about 15 minutes, turning once, until tender and browned in spots. Spread mustard on one side of the broccoli and press into crumbs. Transfer to a platter and sprinkle with any remaining crumbs.