Preheat the oven to 375 degrees F. Spray a small baking sheet with cooking spray.
Bring a medium pot of water to a boil. Add the broccoli and cook until tender-crisp, 3 to 4 minutes. Drain well and blot the broccoli dry with paper towels.
Meanwhile, lay 1 phyllo sheet on a work surface with the long side facing you. Keep the remaining phyllo covered with a clean damp kitchen towel to prevent it from drying out. Lightly spray the phyllo with cooking spray. Continue layering with 9 more phyllo sheets, lightly spraying each sheet with the cooking spray.
Whisk together the mustard, salt, pepper and eggs in a medium bowl. Stir the broccoli and ham into the egg mixture.
Heat the oil in large nonstick skillet over medium heat. Add the egg mixture and cook, stirring with a rubber spatula, until just set, 2 to 3 minutes. Do not overcook. Spoon the egg mixture over the phyllo, leaving a 2-inch border. Sprinkle with the Cheddar. Fold the short sides of the phyllo over the filling and roll up jelly-roll style. Do not roll too tightly.
Place the strudel, seam-side down, on the baking sheet. Lightly spray the strudel with cooking spray. Cut four 1-inch slits in the top to allow the steam to escape. Bake until the filling is hot and the phyllo is golden, about 20 minutes. Let the strudel cool on the baking sheet on a rack at least 10 minutes. Serve warm or at room temperature.
Per Serving: 233 Cal; 16 g Protein; 10 g Tot Fat; 3 g Sat Fat; 4 g Mono Fat; 20 g Carb; 2 g Fiber; 1 g Sugar; 116 mg Calcium; 2 mg Iron; 827 mg Sodium; 177 mg Cholesterol