When filling the background of a header in a drawer component I noticed this gap of white space.
Hello @OLR,
Are you referring to the thin white vertical line between the green background and the greyed-out area to the left of the drawer header?
Or the white space below the header?
Hi Jack,
Just referring to the little git between the green and the greyed out space.
Ahhh I see 
I was playing around with it and set my "Margin" to none, it looks like it fills up to the line but does have super tiny white spots at the top and bottom since it looks like there is somme CSS giving it slightly rounded edges.
I think that might be the closest we can get to not having any border edge separating the colored background with the left side of the drawer.
Custom CSS would be my other guess if the appearance after setting 'Margin' to none is not good enough. Just need to set margin, border and padding to none should override any default style settings.
Hey just did some more testing!
Was looking back at your original picture and it looks like the pixels you highlighted are the 'Border' of the drawer frame. It looks like this can be styled to change the color via the UI.
The red line is "under" that blue line that is highlighting the border of the component.
I couldn't find an option in the UI to remove the border, but this could likely be done with setting border: 0 in custom CSS on the drawer component 
Hope this helps!