Defrost cooked octopus if frozen. Trim the slimy parts off with a sharp knife, rinse, and dry. Grill or broil the octopus so it gets a nice char and that wonderful smoky flavor. Cut on the diagonal in 1/4 inch slices. Set aside.
Boil sliced potatoes until tender but still firm, about 5 to 7 minutes, being careful not to over cook them. Remove to an ice bath to keep them from cooking any further, and drain immediately. Put in a large bowl.
Add bell pepper slices, Serrano slices, celery slices, green onion slices, olives, and capers to the bowl.
Grate lemon zest over the top of everything.
In a glass jar or cruet, make a vinaigrette with the lemon juice, red wine vinegar, rice wine vinegar, and a splash of caper juice. Add the olive oil. Season with salt and pepper and 1/4 teaspoon of Za'atar or oregano. Shake it up,
Add your octopus, chopped basil, and parsley to the bowl. Pour about half of the dressing over the top of everything and toss to combine. Taste and check for seasoning, and add more dressing if desired.
This is equally nice at room temperature or heated through in a frying pan and served warm.