Brostek attended the University of Washington where he lettered in football. Brostek was one of the top offensive linemen in the nation while at Washington, and received numerous honors during his time there.
His honors included:
1988 Rising Award (given to the most outstanding lineman at Washington).
1989 John P. Angel Award (given to the most outstanding offensive lineman at Washington).
Brostek was drafted in the first round of the 1990 NFL Draft by the Los Angeles Rams with the 23rd pick. Brostek played center and guard for the Rams throughout his career. After playing left guard for part of 1991, he replaced Doug Smith as the starting center for the Rams in 1992. Brostek did not miss a down during the 1992 season. He remained the starting center up to the 1996 season. Brostek started every game for the Rams in 4 seasons (1992,1993,1995,1996), including a string of 35 consecutive starts, but, in his final year (1997), he played only a single game. On October 9, 1997, Brostek was placed on the injured reserve list for back problems, and his career ended. In that 1992-1997 span, the Rams never had a winning season, though Brostek blocked for 1,000-yard rushers such as Cleveland Gary and Jerome Bettis. In 1997, the Rams finished in last place in the NFC west division with a won-lost record of 5-11, and he was replaced at starting center by Mike Gruttadauria.