Instructions adapted from:

http://askubuntu.com/questions/6033/enabling-nvidia-driver-messes-up-splash-screen

Add the following to /etc/default/grub (below GRUB_GFXMODE):

GRUB_GFXPAYLOAD_LINUX=1920x1080

Create a file /etc/initframfs-tools/conf.d/splash containing:

FRAMEBUFFER=y

Run the following commands to finish:

sudo update-grub2
sudo update-initramfs -u

After doing this, the Ubuntu splash screen should be 1920×1080 and it should boot directly into that same resolution at the login screen. It will also keep that same resolution as it goes into your graphical session.