Pour about 1 in. water into a large pot and set a steamer basket* in the bottom. Bring to a boil. Add potatoes, reduce heat, and simmer, covered, until tender when pierced, 25 to 30 minutes. Pour potatoes into a colander in the sink, rinse with cool water, and let stand until cool enough to handle.
Peel potatoes and slice crosswise into 1/2-in. thick pieces. Put in a large serving bowl.
In a small bowl, whisk together oil, vinegar, and 3/4 tsp. salt and drizzle over warm potatoes. Sprinkle with chopped herbs and add pepper and additional salt to taste, mixing gently to coat.
*Potatoes cook most evenly in a steamer basket, but if you don't have one, fill pot halfway with water and boil potatoes.
Make ahead: Chill airtight up to 1 day (the salad will become even more flavorful); before serving, bring to room temperature, then stir.