When the C64 gets a soft-reset signal, the first thing it does is check for an EPROM at $8000 (kernal routine $FD02). We can take advantage of this routine to redirect resets to our own code.

  * = $0900
  sei
  lda #$c3 ;the string "CBM80" at $8004 is used to check 8-ROM
  sta $8004
  lda #$c2
  sta $8005
  lda #$cd
  sta $8006
  lda #$38
  sta $8007
  lda #$30
  sta $8008
  lda #<reset ;redirect the vector at $8000 to our own code
  sta $8000
  lda #>reset
  sta $8001
main
  inc $d020 ;just something to look at
  jmp *-3

reset
  lda #$2f ;reset data-direction register, otherwise the system won't start correctly
  sta $00
  jsr $e5a8 ;optional, refresh the VIC
  jmp main ;go back to main code

Now try soft-resetting. Instead of going back to the basic screen, instead you'll see the inc $d020 effect.

Note that if you're using the kernal NMI routine ($FE47), also redirect the vector at $8002.