Casserole: In large pot of boiling salted water, cook pasta until tender but firm, about 8 minutes. Drain and rinse with cold water; set aside.
Remove florets from broccoli and set aside. Using knife, remove any hard knobs from broccoli stems. Chop stem to produce 1 cup (250 mL) of stem bits.
In boiling salted water, add stem bits and cook for 4 minutes, add broccoli florets and continue cooking 3 minutes longer, drain all broccoli and rinse with cold water.
Scatter pasta, hard-cooked eggs, broccoli, ham and green onions evenly into six ( 2 cup/500 mL) oval gratin dishes.
Cheese Sauce: In saucepan, heat butter over medium-low heat, add flour and cook, stirring to make a roux or paste, about 2 minutes.
Whisk in milk and cook, continue whisking until thickened, about 6 minutes. Remove from heat and stir in cheese, mustard powder, salt and pepper. Continue whisking until cheese is melted, about 4 minutes.
Pour cheese sauce over gratin dishes. Sprinkle remaining cheddar cheese and parsley over the gratin dishes. Place dishes on large rimmed baking sheet and bake in 375ºF (190ºC ) oven until heated through and cheese is melted, about 20 minutes. (Make ahead: Cover and refrigerate for up to 2 days. Increase cooking time by 10 minutes.)
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