Country Club Towers II, a new twin-tower apartment complex planned for Denver's Washington Park neighborhood near Cherry Creek, will break ground May 29, making it the newest project in Pat Broe's multi-state empire. The project, at 1001 E. Bayaud Ave. between South Downing and Ogden streets, will add 552 apartment units to the area in two 30-story towers that raised ire among neighbors when they heard the news of the development in September. Neighborhood groups like the Alamo Placita Neighborhood…