This is completely dependent on the machine you're running your code on. Commodore 64 again? Please put this in the subject, or at least in the post. My psychic powers have limits.
BRK is a software-generated interrupt. The C64's interrupt handler starts at $FF48. The first thing it does after pushing registers is look at the B flag. If it's clear it jumps through the vector CINV at $0314. If it's set (because we got here from a BRK instruction) it jumps through the vector CBINV at $0316. Point CBINV at your handler, and you can do whatever you like. Your handler will have to pop the registers before returning, and there's a handy snippet of code at $EA81 that will do it for you.
But doing that will return to your program. If you wanted to warm-start BASIC without clearing the screen, JMP ($A002) will probably do it. If you've changed any VIC registers JSR PANIC ($E5A0) will reset them.
I'm using the very useful KERNAL and BASIC source code posted by Michael Steil at
https://github.com/mist64/c64ref/blob/master/c64disasm/c64disasm_cbm.txt and
https://github.com/mist64/c64ref/blob/master/c64disasm/c64disasm_ms.txt