I've played around with the Shadows settings under the Render tab, but I still have some shadow jaggies on my object lit only from an HDRI.
Hey cash_flagg, HDRs can't cast shadows in Eevee. There's some workarounds for this, obviously you can use the irradiance volume to bake lighting, or use lamps to simulate the hdr. Double check to see if the shadows in your scene are being cast by a light that you forgot about!