Lightly coat the inside of a 6-quart slow cooker with cooking spray. Stir together evaporated milk, milk, and water in its bowl. Sprinkle flour on top and whisk constantly until smooth. Stir in mustard, salt, pepper, 2 cups cheddar, Monterey jack, and Parmesan. Fold in macaroni and broccoli, making sure the macaroni is immersed in liquid.
Cover and cook on high until pasta is tender and most of liquid is absorbed, 2 hours. Remove cover and stir mixture until it comes together. Sprinkle remaining 1/2 cup cheddar cheese evenly over top. Cover and cook 15 minutes more. Garnish with paprika if desired.