Look in C:\Program Files (x86)\Brother\BrLauncher for a file with the .ini extension that has the same name as your scanner.  In my case the file was C:\Program Files (x86)\Brother\BrLauncher\HL-2930DW LAN.ini

Open the ini file and look for the section heading named [SCAN]. Under the [SCAN] section there should be a line for the Control Center Scan function that looks similar to this one (your model may be different):
ControlCenter_Scan=C:\Program Files (x86)\ControlCenter4\BrCcBoot.exe /model="HL-L2390DW LAN" /OpenTab=0x01

Copy everything from this line after the = sign to the end of this line and paste it into a new shortcut.
When you create your new shortcut you will need to edit the pasted line and put quotes around the path to the executable so that it looks similar this (your model may be different):
"C:\Program Files (x86)\ControlCenter4\BrCcBoot.exe" /model="HL-L2390DW LAN" /OpenTab=0x01
Your new shortcut will directly open the Control Center 4 Scan page.

I don't have the Control Center configured to run on start up and the new shortcut works fine. It can be closed and restarted without issues.  I hope this works for you too.