Bring 3 quarts water to boil in large saucepan over high heat.
Add potatoes and 3 tablespoons salt; return to boil and cook until potatoes are very tender and easily crushed but not breaking down, 20 to 25 minutes.
Drain potatoes in colander and let sit until cool enough to handle but still warm, about 10 minutes.
Wipe saucepan clean with damp paper towels.
Heat oil and garlic in now-empty saucepan over medium heat, swirling oil constantly once garlic begins to sizzle.
Cook until garlic is light golden brown, 3 to 5 minutes.
Immediately pour oil and garlic into large bowl.
Add mayonnaise, vinegar, pepper, and salt and whisk until smooth.
Using your fingertips, gently tear each potato into rough 1-inch pieces and add to bowl with dressing.
Add herbs and toss until evenly combined.
Season with salt, pepper, and extra vinegar to taste.
Serve warm, at room temperature, or chilled.
(Potato salad can be refrigerated for up to 3 days; season with salt, pepper, and vinegar to taste before serving.)
