I think there are posts about other empanadas places (wait, I think I have even written a few) but it is late for me so I will just tell you . . . got to El Mercado, the corner shop at Southport & Grace, it is connected via family to Tango Sur next door. They have empanadas, for sale in a little hot case by the cash register, to stop you in your tracks and stop your heart if you eat too many. I like the beef over the chicken but have been known to snarf down a pollo version happily. I have never had any sauce with them as I am almost always eating them vertically (standing, walking) or vehicularly (driving). They now serve both baked and fried versions and I like both, but um, er, prefer the fried. I am told they serve the same at the restaurant and also at the bar their son runs on Elston.
Another place that doesn't get a lot of love here is La Fonda on Broadway in Edgewater. I think their empanadas are lovely, they too do both fried and baked versions and they have 2 different green sauces to compliment them. And then there is, of course, El Nandu over on Fullerton in Logan Square . . . is it still open? If it is, the empanadas were my go to item on their menu but I haven't been for years.
I know I am kind of all over the map and a bit vague but it might get you started.
bjt
"eating is an agricultural act" wendell berry