How to draw Pixels in high resolution (1920x1080 or 1366x768) on screen in protected mode using x86 ASM or C?

Question

I am trying to build a Hobby Operating System and I have successfully built my own two stage bootloader which handles control to the kernel after switching to protected mode. I am able to display characters on the screen by writing at 0x000B0000 - 0x000B7777. Now I want to draw individual pixels on the screen. I want to control pixels at the native resolution of my monitor(1366x768) and not at some downscaled resolution like 640x320. I wanted to ask how this is done in a real Operating System like Windows or Linux. Also some guidance on VESA BIOS Extensions would be helpful although I don't want to use VBE.