Medium is distorted Brothers.

Your best chance is may be asking directly Adam Trageser but I'm afraid the answer would be (part of 'MEDIUM') mostly hand-drawn or so much customized that to me it would be quite helpless to know the original font. I'd risk some though Sackers Gothic for '& COMPANY' and the usual Letterhead/Billhead for 'THE FINEST QUALITY'. But as said, would need a lot of customization to get only loosely close.
Now some food for the mind: Jon Contino, Decade Type Foundry, Letterhead Fonts, Artist of Design, Magpie Paper Works, Great Lakes Lettering, Fontscafe, Greater Albion Typefounders, Kimmy Design, Coffee Bin Fonts, Solotype, Lost Type Co-op, tons of resources on Creative Market

EDIT: links fixed. Thx Don.

Rare is indeed rare. After digging through my usual suspects, including those listed by Ryuk, plus P-22, T-24, HiH, Wiesher and Spiece Graphics I still did not spot it. Either I missed it in my quick scanning, or it's elsewhere -- if it's a font.
Don

Rare looks so incredibly familiar and yet ... I dunno.

Funny because the only one that reminds me of nothing is 'RARE' :D. Looks too much deconstructed/eroded/manipulated/distorted to be something else than hand-drawn (and rather close actually to Jon Contino's lettering style) and mixing style of Windsor and 'Grant' Grants Antique/Sheridan Gothic/Refugio/Grant Rustic.
Actually, Sheridan Gothic/Refugio Rustic/Grant Rustic might be good substitutes for 'THE FINEST QUALITY'.

Hy Ryuk, note that you have broken links for Decade Type Foundry, Creative Market.
Don

RARE. As it appears that this is a well hidden font, or not a font at all, the question is whether you would like to have an alphabet with similar style. Some of the letters, such as the flat top A could be derived from the list posted by Ryuk. The swoop for the upper bowl of R, and similar letters such as B, C and P could be modeled on Sveva http://www.myfonts.com/fonts/astype/sveva-as-versal/. Big bowls on Windsor, Milton etc.
Don