Place potatoes on a foil-lined baking sheet. Bake at 450° for 50 minutes or until tender. Let stand 10 minutes.
Heat a saucepan over medium heat. Add oil; swirl to coat. Add ham; sauté 3 minutes or until lightly browned. Add onion to pan; sauté 2 minutes. Combine 1/4 cup milk and flour in a small bowl, stirring with a whisk. Add flour mixture and remaining 3/4 cup milk to pan, stirring constantly with a whisk. Cook 4 minutes or until slightly thickened. Remove pan from heat. Stir in mustard, salt, pepper, and cheese.
Bring 2 cups water to a boil in a medium saucepan. Add broccoli; cook 4 minutes or until crisp-tender. Drain.
Cut a lengthwise slit in each potato. Gently squeeze potatoes at both ends to open. Divide broccoli among potatoes; top evenly with sauce.