Here is a photo of our situation! Thank you again for any advice you may have for us!

How do you plan to insulate the space to current code requirements? As shown, it is R 0, and will let all of your heat escape.

I think it is really a personal preference based upon how you plan to decorate your home. I would suggest you do a Houzz search in the above search bar for exposed beams in cathedral ceiling. There are lots of photos. IMO only, when you paint them white it loses any impact and starts to look like a porch area. If you do decide to have an exposed beam, you still need to wrap (box in) your LVL with some type of wood product - then you could paint or stain.

The ceiling is not done we are in the process as we speak.
From the pic the drywall will be another 7" down from the existing 2x6 for the insulation and air gap.

We were thinking of not having the beam exposed at all to give a cleaner look but decided to keep the beam exposed

7'' isn't nearly enough for an air gap and the required amount of insulation. Your inspector can red flag you for that.

Actually the 12 + inches you will have will be enough for r40 single batt insulation with a 2 inch air space. I would hide the whole beam. keeping it partially exposed would show only about 3 inches of the besm