Charcoal, looks like black from a distance but doesn’t get as hot.

I would go with a medium gray or charcoal. Always looks good and is neutral. It would also work nicely with your black door/shutters.

Driftwood is nicer balance between top & bottom materials. It has some warm tones mixed in it to work with your warm toned brick. Blacks, charcoals, & grays can skew roofs blue-ish & cold because of sky reflection. My rendering makes this look more textured than it really is:

Charcoal is too top heavy looking:

Pretty house, btw!

Thank you @awm03 for these examples. The driftwood definitely looks better but do you still like it with the black shutters? Any other colors you would look at? I saw this example house but don’t know what color this roof is...looks more gray and less brown than driftwood?

The driftwood shingles will look fine with black shutters.

The thing is, though, if you look at your house, the largest planes are the roof and the siding. They have to
relate. So don't worry about matching the roof to the shutters. Worry
instead about the roof & the siding (brick, right?) working
together. The shutters are just accent color, are tiny compared to the
roof & siding surfaces, and you have more leeway for color
experiments there. But the siding & the roof have absolutely have
to work together.

In your example picture: the house is in shadow,
so the colors are muted and look cool toned. That roof/siding combo
probably looks a bit off with the sun shining on it, as the lighting
changes with the time of day or weather. But if you stick with a roof
that has warm tones mixed in or is a warm tone overall, it will
harmonize with your brick regardless of the light.

Looks like the
driftwood shingles have enough gray blended in that the roof doesn't
read totally brown, if that's what you're hesitant about.

Here are some all gray blends:

Not awful, but not as nice as a brown/gray blend like Driftwood.

I don't think I'd ever get a black or very dark roof, certainly not anywhere south of, say, Minnesota. It raises summer temperatures in the attic. That causes faster roof degradation. It also makes the house hotter and/or increases air conditioning costs.

If I had a house like yours, in Certainteed I'd probably choose Sandstone or Birchwood, maybe even Mist White. But then I'm not a decorator, just a frugal homeowner. :)