Gorgeous Bullion Eagle!
This a 1920s-30s full dress hat for a company grade artillery officer. For those who may not know, company grade are the ranks 2nd and 1st Lieutenants and Captains (Field grade would be Major, Lt. and full Colonel). Sorry for the lesson.
This is a gorgeous hat with light fading to the bullion, and overall for that matter. The sweatband appears to be a replacement but a nice job was done putting it in. The size label on the band says 6 7/8 and would be accurate. Made by Basch Cap Company, Boston, Mass. I am not familiar with this firm and could be a scarce maker of military headgear.