Although appearing less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year—they are often green and striped, or have plenty of bumps and bruises—heirlooms are more flavorful and thus in increasing demand.

The non-underlined part within the two dashes explains heirloom tomatoes. 
After the dash, we have a clause that says heirloom tomatoes are more flavorful and thus in increasing demand. As “although” is used for contradiction, we need to have a clause that denotes something negative about heirloom tomatoes in the first clause.

(A) Although appearing less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year
There is no corresponding verb for “heirloom tomatoes”. Eliminate.

(B) Although heirloom tomatoes, grown from seeds saved during the previous year, appear less appetizing than most of their round and red supermarket cousins
Correct

(C) Although they appear less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year
Same as A. 

(D) Grown from seeds saved during the previous year, heirloom tomatoes appear less appetizing than most of their round and red supermarket cousins
There’s no punctuation or conjunction that suggests a contrast in the sentence. Eliminate

(E) Heirloom tomatoes, grown from seeds saved during the previous year, although they appear less appetizing than most of their round and red supermarket cousins

The placement of the subordinating conjunction “although” is faulty. 
There is no corresponding verb for “heirloom tomatoes”. Eliminate.