Most of the "PC rolls only" systems I know of use roll-over dice conventions: players roll dice, add modifiers based on their own abilities and assets, and try to match or exceed a Difficulty Number set by the GM. If you're willing to re-work all skills as bonuses on a percentile (or d20?) roll, that may be the way to go. You'd have to distinguish +0% from "no skill", re-think difficulty numbers for normally un-opposed rolls, and re-define experience rolls (e.g. skill + die < 100%).
The most BRP-ish system I can think of would use an extremely coarse-grained system: to hit or parry "average" foes require only a normal success, while more challenging foes may require a "special" or even "critical" success just to hit. One could also use the Easy - Average - Hard modifiers from BRP (double or half skill), or the bonus/penalty die from COC7 (roll two "tens" dice, and pick the higher or lower depending on whether the player has a penalty or bonus to his action).
None of this will yield the same probabilities as the old two-dice system, and I doubt they'd even be close. But I think these options play faster at the table and/or follow the "BRP Way".
"A hidden corridor! Fortunately it was labeled!" -- Sadie Doyle, "Beyond Belief: Sarcophagus Now", The Thrilling Adventure Hour