Pierce potatoes several times with fork. Place in microwave oven on paper towel. Microwave on HIGH 15 minutes or just until softened. Wrap in paper towels; let stand 5 minutes.
Bring water to a boil in medium saucepan over medium heat. Add broccoli. Cook 5 minutes or until broccoli is crisp-tender. Drain. Add milk, cottage cheese, mustard and red pepper flakes to broccoli in saucepan. Bring to a boil. Reduce heat to medium-low; remove from heat.
Combine 3/4 cup cheddar cheese, mozzarella cheese and flour in medium bowl. Toss to coat cheese with flour; add to broccoli mixture. Cook and stir over medium-low heat until cheese is melted and mixture is thickened.
Cut potatoes open. Divide broccoli mixture evenly among potatoes. Sprinkle with remainig 1/4 cup cheddar cheese.