Boil potatoes in a large saucepan of water set over high just until fork-tender, 12 to 15 min. Drain and cover with cold water until cool, about 5 min.

Massage cucumbers with 1/4 tsp salt  until thoroughly mixed in a large bowl. Let stand until liquid begins to seep out, 10 min. Scoop cucumbers into a strainer and squeeze out excess liquid.

Whisk oil with vinegar and remaining  1/2 tsp salt in same bowl. Season with fresh pepper. Add parsley, dill, cucumbers and potatoes. Toss until well coated.