Mirrored values in the testbench are copies of DUT register values observed by looking at transactions on the bus connected to the DUT(frontdoor), or looking at signals directly inside the DUT(backdoor). Your testbench uses the mirrored values for quick access to make decisions on stimulus to the DUT and for the scoreboard to make decisions on expected results.
Desired values of registers in the testbench is a way to change the values of registers in the DUT. Frontdoor access will generate stimulus to set the register in the DUT, and backdoor access will set the registers directly without any stimulus.
An easy way to create a test is to set all the desired registered values and see that the mirrored values get updated to match the desired.