Right at the intersection of Milwaukie Ave. and Bybee in Sellwood, you'll find the Oaks Bottom Public House.
Not really a pub, but more of a grill with a ton of local beers. Their menu offers six burger options,(basic, with cheese, bacon) and then a few gourmet twists. Having had tried their Jalapeno burger previously, and being pretty happy with it, this time around i stepped to the 1/2 pound chevre burg.
I wasn't given the option of how I wanted it cooked, and I would have enjoyed it a bit rarer, but the sheer amount of amazing chevre cheese piled high really negated any other areas I could find fault. It was a pretty damn fine sando. Recommended.
Also of note was the option to accompany any burger with what I found to be the best tots i've tasted in a long time.
PS: Try some of the Ninkasi brews from eugene.
Oaks Bottom Public House
1621 SE Bybee
Portland, OR 97202